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Domain & Range

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Wize University Calculus 1 Textbook > Pre-Calculus (Review)

Operations with Functions

4 Activities

Wize University Calculus 1 Textbook > Pre-Calculus (Review)

Radical Functions

4 Activities

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Practice: Domain & Range

If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
More Operations with Functions Questions:
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Q:\bf{Q:} Find f(g(x))f(g(x)) and its domain if f(x)=1x−1f\left(x\right)=\dfrac{1}{x-1} and g(x)=1x+2g\left(x\right)=\dfrac{1}{x+2}
Let f(x)f(x) and g(x)g(x) be two functions with values given in the following table:
The value of f(g(2))+g(f(2))f\left(g\left(2\right)\right)+g\left(f\left(2\right)\right) is:
Q:\bf{Q:} State the possible values of ff and gg given f(g(x))=x−ln⁡xf\left(g\left(x\right)\right)=\sqrt{x-\ln x}
Function Operations
Let f(x)=xx−3f(x)=\dfrac{x}{x-3} and let g(x)=22x+1g(x)=\dfrac{2}{2x+1}.
Determine the following, simplifying all answers (leave answer in factored form where possible):
Operations with Functions
Practice: Operations with Functions
George sells boxes of chocolates at the Ladner Market. It costs $550/month to run the stand plus an additional cost of $4.45/box for supplies. George sells a box of half-dozen chocolates for $8.95/box.
Note: Let 'x' be the number of boxes of chocolates sold.
Operations with Functions
Practice: Operations with Functions
Amy owns a skincare company. Her biggest seller is her "Rose oil Face Cream". Her fixed monthly costs are $1600/month plus an additional $12/jar for all supplies and ingredients. Amy charges $45/4oz jar of face cream.
Note: Let 'x' be the number of jars that will be sold.
Operations with Functions
Practice: Operations with Functions
Let f(x)=4x2+12x+9f(x)=4x^2+12x+9 and g(x)=4x2+4x−3g(x)=4x^2+4x-3.
Determine f(x)g(x)\dfrac{f(x)}{g(x)}.
Operations with Functions
Practice: Operations with Functions
Let f(x)=25x2+30x+25f(x)=25x^2+30x+25 and g(x)=5x+3g(x)=5x+3.
Determine f(x)g(x)\dfrac{f(x)}{g(x)}
Operations with Functions
Practice: Operations with Functions
The graphs of f(x)f(x) (in green) and g(x)g(x) (in blue) are provided on the same plot shown below:
Operations with Functions
Practice: Operations with Functions
The graphs of f(x)f(x) (in green) and g(x)g(x) (in blue) are provided on the same plot shown below:
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Let f(x)f(x) and g(x)g(x) be two functions with values given in the following table:
The value of f(g(2))+g(f(2))f\left(g\left(2\right)\right)+g\left(f\left(2\right)\right) is:
Q:\bf{Q:} Find f(g(x))f(g(x)) and its domain if f(x)=1x−1f\left(x\right)=\dfrac{1}{x-1} and g(x)=1x+2g\left(x\right)=\dfrac{1}{x+2}
Q:\bf{Q:} State the possible values of ff and gg given f(g(x))=x−ln⁡xf\left(g\left(x\right)\right)=\sqrt{x-\ln x}
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Operations with Functions
Consider the functionsf(x)=x23−x2f(x)=\frac{x^2}{\sqrt{3-x^2}} and g(x)=6−xg(x)=\sqrt{6-x}. Find the domain of (f∘g)(x)(f \circ g)(x).
Practice: Functions Properties
Practice: Function Properties
If f(x)=∣x−2∣, g(x)=3−x+1f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}, which of the following is true about h(x)=g(f(x))h\left(x\right)=g\left(f\left(x\right)\right)?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
More Radical Functions Questions:
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Absolute Value Functions: Function Properties
If f(x)=∣x−2∣, g(x)=3−x+1f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}, which of the following is true about h(x)=g(f(x))h\left(x\right)=g\left(f\left(x\right)\right)?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Radical Functions
State the domain and range of the function f(x)=1x2−4f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}.
Consider the functions f(x)=x25−x2f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}} and g(x)=2−xg\left(x\right)=\sqrt{2-x}
a. Find (f∘g)(x)(f \circ g)(x)
b. Find the domain of (f∘g)(x)(f \circ g)(x) . Enter in interval notation.
Radical Functions
Find the domain of f(x)=1x2−4−3f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
Radical Functions
Solve for xx:
3x3−3x2+1=x^3\sqrt{x^{3}-3x^2}+1=x
Solving Radical Equations
Solve for a:
2a+4−3=3a−22\sqrt{a+4}-3=\sqrt{3a-2}
Solving Radical Equations
Solve for xx:
2x−1=x\sqrt{2x-1}=\sqrt{x}
Radical Functions
Graph the function y=−34(x−2)+3y=-3\sqrt{4(x-2)}+3.
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x−6+3=x+9\sqrt{x-6}+3=\sqrt{x+9}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x2−2=x+4\sqrt{x^2-2}=\sqrt{x+4}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on xx:
10+10x−1=13\begin{array}{rcl} 10+\sqrt{10x-1}&=&13 \end{array}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on xx:
x−3=3x−4\begin{array}{rcl} x-3&=&3\sqrt{x-4} \end{array}
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=−−3x+6−2y=-\sqrt{-3x+6}-2?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=4x−1y=\sqrt{4x}-1?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Absolute Value Functions: Function Properties
If f(x)=∣x−2∣, g(x)=3−x+1f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}, which of the following is true about h(x)=g(f(x))h\left(x\right)=g\left(f\left(x\right)\right)?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Consider the functions f(x)=x25−x2f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}} and g(x)=2−xg\left(x\right)=\sqrt{2-x}
a. Find (f∘g)(x)(f \circ g)(x)
b. Find the domain of (f∘g)(x)(f \circ g)(x) . Enter in interval notation.
Radical Functions
Find the domain of f(x)=1x2−4−3f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
Radical Functions
State the domain and range of the function f(x)=1x2−4f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}.
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Radical Functions
Given the function g(x)=3+5+7xg\left(x\right)=3+\sqrt{5+7x}
Fill in the blanks using the following options:
{x : x<75},  {x : x≥75} ,  {x : x≤75} , {x : x>75} \left\{x\ :\ x<\frac{7}{5}\right\},\ \ \left\{x\ :\ x\ge\frac{7}{5}\right\}\ ,\ \ \left\{x\ :\ x\le\frac{7}{5}\right\}\ ,\ \left\{x\ :\ x>\frac{7}{5}\right\}\