Answer
(a) 3
(b) $g$ is one-to-one because for any two x-coordinates $x_1$ and $x_2$, $g(x_1) \neq g(x_2)$
(c) 0.2
(d) $[-1,3.5]$
(e) We can see a sketch of the graph of $g^{-1}$ below.
Work Step by Step
(a) On the graph, we can see that $g(2) = 3$
(b) $g$ is one-to-one because for any two x-coordinates $x_1$ and $x_2$, $g(x_1) \neq g(x_2)$. Note that $g$ is an increasing function. Since the function is increasing, for any two x-coordinates $x_1$ and $x_2$, $g(x_1) \neq g(x_2)$.
(c) $g(0.2) = 2$
Then: $g^{-1}(2) = 0.2$
(d) The domain of $g^{-1}$ is the range of $g$.
The range of $g$ is $[-1,3.5]$
The domain of $g^{-1}$ is $[-1,3.5]$
(e) We can find some coordinate pairs in the graph of $g$:
$(-2,-1)$
$(0,1)$
$(1,2.6)$
$(2,3)$
$(4,3.5)$
In the graph of $g^{-1}$, these coordinate pairs are reversed:
$(-1,-2)$
$(1,0)$
$(2.6,1)$
$(3,2)$
$(3.5,4)$
We can see a sketch of the graph of $g^{-1}$ below.
