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Let f(x) and g(x) be two functions with values given in the following table: Th…
Related Topics
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Operations with Functions
4 Activities
Let
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
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)
f
(
g
(
2
)
)
+
g
(
f
(
2
)
)
is:
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
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Check Submission
More Operations with Functions Questions:
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Function composition
Consider the functions
f
(
x
)
=
x
1
/
2
3
−
x
f(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}}
f
(
x
)
=
3
−
x
x
1/2
and
g
(
x
)
=
(
6
−
x
)
2
g(x)=(6-x)^2
g
(
x
)
=
(
6
−
x
)
2
. Find
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
and the domain.
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Q
:
\bf{Q:}
Q
:
Find
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
and its domain if
f
(
x
)
=
1
x
−
1
f\left(x\right)=\dfrac{1}{x-1}
f
(
x
)
=
x
−
1
1
and
g
(
x
)
=
1
x
+
2
g\left(x\right)=\dfrac{1}{x+2}
g
(
x
)
=
x
+
2
1
Let
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
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)
f
(
g
(
2
)
)
+
g
(
f
(
2
)
)
is:
Q
:
\bf{Q:}
Q
:
State the possible values of
f
f
f
and
g
g
g
given
f
(
g
(
x
)
)
=
x
−
ln
x
f\left(g\left(x\right)\right)=\sqrt{x-\ln x}
f
(
g
(
x
)
)
=
x
−
ln
x
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Function Operations
Let
f
(
x
)
=
x
x
−
3
f(x)=\dfrac{x}{x-3}
f
(
x
)
=
x
−
3
x
and let
g
(
x
)
=
2
2
x
+
1
g(x)=\dfrac{2}{2x+1}
g
(
x
)
=
2
x
+
1
2
.
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
)
=
4
x
2
+
12
x
+
9
f(x)=4x^2+12x+9
f
(
x
)
=
4
x
2
+
12
x
+
9
and
g
(
x
)
=
4
x
2
+
4
x
−
3
g(x)=4x^2+4x-3
g
(
x
)
=
4
x
2
+
4
x
−
3
.
Determine
f
(
x
)
g
(
x
)
\dfrac{f(x)}{g(x)}
g
(
x
)
f
(
x
)
.
Operations with Functions
Practice: Operations with Functions
Let
f
(
x
)
=
25
x
2
+
30
x
+
25
f(x)=25x^2+30x+25
f
(
x
)
=
25
x
2
+
30
x
+
25
and
g
(
x
)
=
5
x
+
3
g(x)=5x+3
g
(
x
)
=
5
x
+
3
.
Determine
f
(
x
)
g
(
x
)
\dfrac{f(x)}{g(x)}
g
(
x
)
f
(
x
)
Operations with Functions
Practice: Operations with Functions
The graphs of
f
(
x
)
f(x)
f
(
x
)
(in green) and
g
(
x
)
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)
f
(
x
)
(in green) and
g
(
x
)
g(x)
g
(
x
)
(in blue) are provided on the same plot shown below:
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Q
:
\bf{Q:}
Q
:
Find
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
and its domain if
f
(
x
)
=
1
x
−
1
f\left(x\right)=\dfrac{1}{x-1}
f
(
x
)
=
x
−
1
1
and
g
(
x
)
=
1
x
+
2
g\left(x\right)=\dfrac{1}{x+2}
g
(
x
)
=
x
+
2
1
Q
:
\bf{Q:}
Q
:
State the possible values of
f
f
f
and
g
g
g
given
f
(
g
(
x
)
)
=
x
−
ln
x
f\left(g\left(x\right)\right)=\sqrt{x-\ln x}
f
(
g
(
x
)
)
=
x
−
ln
x
Function composition
Consider the functions
f
(
x
)
=
x
1
/
2
3
−
x
f(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}}
f
(
x
)
=
3
−
x
x
1/2
and
g
(
x
)
=
(
6
−
x
)
2
g(x)=(6-x)^2
g
(
x
)
=
(
6
−
x
)
2
. Find
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
and the domain.
Operations with Functions
Consider the functions
f
(
x
)
=
x
2
3
−
x
2
f(x)=\frac{x^2}{\sqrt{3-x^2}}
f
(
x
)
=
3
−
x
2
x
2
and
g
(
x
)
=
6
−
x
g(x)=\sqrt{6-x}
g
(
x
)
=
6
−
x
. Find the domain of
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
.
Practice: Functions Properties
Practice: Function Properties
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
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)
h
(
x
)
=
g
(
f
(
x
)
)
?
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
