Question

consider the graph of the function $f(x)$ below.
what is the value of $f^{-1}(2)$?

Explanation:

Step1: Recall inverse function definition

$f^{-1}(a)=b$ means $f(b)=a$

Step2: Find x where f(x)=2

We first identify the equation of $f(x)$. The line passes through $(0,-1)$ and $(1,0)$, so slope $m=\frac{0-(-1)}{1-0}=1$. The equation is $f(x)=x-1$. Set $f(x)=2$:
$$x-1=2$$

Step3: Solve for x

$$x=2+1=3$$
Thus $f^{-1}(2)=3$.

Answer:

3