Answer
a. $1$
b. $2$
c. $5$
d. $0$
e. $1$
f. $2$
g. $2$
h. $5$
Work Step by Step
a. $f(0)$
The order pair for the function is
$=(x,f(x))$
Substitute $x=0$.
$=(0,f(0))$
From the graph we have
$=(0,1)$
Hence, the correct answer is $f(0)=1$.
b. $f(1)$
The order pair for the function is
$=(x,f(x))$
Substitute $x=1$.
$=(1,f(1))$
From the graph we have
$=(1,2)$
Hence, the correct answer is $f(1)=2$.
c. $f(2)$
The order pair for the function is
$=(x,f(x))$
Substitute $x=2$.
$=(2,f(2))$
From the graph we have
$=(2,5)$
Hence, the correct answer is $f(2)=5$.
d. $f^{-1}(1)$
The order pair for the function is
$=(x,f^{-1}(x))$
Substitute $x=1$.
$=(1,f^{-1}(1))$
From the graph we have
$=(1,0)$
Hence, the correct answer is $f^{-1}(1)=0$.
e. $f^{-1}(2)$
The order pair for the function is
$=(x,f^{-1}(x))$
Substitute $x=2$.
$=(2,f^{-1}(2))$
From the graph we have
$=(2,1)$
Hence, the correct answer is $f^{-1}(2)=1$.
f. $f^{-1}(5)$
The order pair for the function is
$=(x,f^{-1}(x))$
Substitute $x=5$.
$=(5,f^{-1}(5))$
From the graph we have
$=(5,2)$
Hence, the correct answer is $f^{-1}(5)=2$.
g. $f^{-1}[f(2)]$
Substitute $f(2)=5$
$f^{-1}(5)$
The order pair for the function is
$=(x,f^{-1}(x))$
Substitute $x=5$.
$=(5,f^{-1}(5))$
From the graph we have
$=(5,2)$
Hence, the correct answer is $f^{-1}(5)=2$.
h. $f[f^{-1}(5)]$
Substitute $f^{-1}(5)=2$
$f(2)$
The order pair for the function is
$=(x,f(x))$
Substitute $x=2$.
$=(2,f(2))$
From the graph we have
$=(2,5)$
Hence, the correct answer is $f(2)=5$.
