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Function Operations

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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):



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}
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).
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 Operations with Functions Questions:
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:
More Operations with Functions Questions:
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:
More Operations with Functions Questions:
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: