합성함수와 역함수

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate each expression.

$x$	$f(x)$	$g(x)$
0	7	9
1	6	5
2	5	6
3	8	2
4	4	1
5	0	8
6	2	7
7	1	3
8	9	4
9	3	0

$g(g(2))$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate each expression.

$x$	$f(x)$	$g(x)$
0	7	9
1	6	5
2	5	6
3	8	2
4	4	1
5	0	8
6	2	7
7	1	3
8	9	4
9	3	0

$g(g(6))$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(f\circ g)(1)$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(f\circ g)(2)$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(g\circ f)(2)$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(g\circ f)(3)$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(g\circ g)(1)$

For the following exercises, use the function values for $f\text{ and }g$ shown in (the referenced table) to evaluate the expressions.

$x$	$f(x)$	$g(x)$
-3	11	-8
-2	9	-3
-1	7	0
0	5	1
1	3	0
2	1	-3
3	-1	-8

$(f\circ f)(3)$

For the following exercises, use each pair of functions to find $f(g(0))$ and $g(f(0)).$

$f(x)=4x+8,\,g(x)=7-{x}^{2}$

For the following exercises, use each pair of functions to find $f(g(0))$ and $g(f(0)).$

$f(x)=5x+7,\,g(x)=4-2{x}^{2}$

For the following exercises, use each pair of functions to find $f(g(0))$ and $g(f(0)).$

$f(x)=\sqrt{x+4},\,g(x)=12-{x}^{3}$

For the following exercises, use each pair of functions to find $f(g(0))$ and $g(f(0)).$

$f(x)=\frac{1}{x+2},\,g(x)=4x+3$

For the following exercises, use the functions $f(x)=2{x}^{2}+1$ and $g(x)=3x+5$ to evaluate or find the composite function as indicated.

$f(g(2))$

For the following exercises, use the functions $f(x)=2{x}^{2}+1$ and $g(x)=3x+5$ to evaluate or find the composite function as indicated.

$f(g(x))$

For the following exercises, use the functions $f(x)=2{x}^{2}+1$ and $g(x)=3x+5$ to evaluate or find the composite function as indicated.

$g(f(-3))$

For the following exercises, use the functions $f(x)=2{x}^{2}+1$ and $g(x)=3x+5$ to evaluate or find the composite function as indicated.

$(g\circ g)(x)$

For the following exercises, use $f(x)={x}^{3}+1$ and $g(x)=\sqrt[3]{x-1}.$

Find $(f\circ g)(x)$ and $(g\circ f)(x).$ Compare the two answers.

For the following exercises, use $f(x)={x}^{3}+1$ and $g(x)=\sqrt[3]{x-1}.$

Find $(f\circ g)(2)$ and $(g\circ f)(2).$

For the following exercises, use $f(x)={x}^{3}+1$ and $g(x)=\sqrt[3]{x-1}.$

What is the domain of $(g\circ f)(x)?$

For the following exercises, use $f(x)={x}^{3}+1$ and $g(x)=\sqrt[3]{x-1}.$

What is the domain of $(f\circ g)(x)?$