Question

Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3

Answer 1

In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).

So we have:

`\begin{gathered} f(x)=(x+3)^2 \\ x=(f^(-1)(x)+3)^2 \\ \sqrt[]{x}=f^(-1)(x)+3 \\ f^(-1)(x)=-3+\sqrt[]{x} \end{gathered}`

(The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)

In order to graph the function and its inverse, we can use some points that are solutions to each one.

For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).

For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).

Graphing f(x) in red and f^-1(x) in blue, we have:

Graphing it manually, we have: