Question

The graph of the invertible function f is shown on the grid below.

Answer 1

We have been given graph of function $y=f(x)$. We are asked to find the value of $f^{-1}(6)$ from the graph of  $y=f(x)$.

We know that to find an inverse function is a function that reverses another function. A function f(x) gives an output of y, when we input some value of x. The inverse of f(x) will give the same value of x from value of y.

So to find inverse of a function we need to switch all x and y values.

We can see that $f(4)=6$, so to to find value of  $f^{-1}(6)$, we have to switch x and y values.

After switching x and y values, we will get:

$f^{-1}(6)=4$

Therefore, $f^{-1}(6)=4$.