Question

What is the inverse of f(x) = (x - 5)^2 for x ≥ 5 where function g is the inverse of function f?A) g(x) = ✓x - 5, x ≥ 0B) g(x) = ✓x - 5, x ≥ 5C) g(x) = ✓x + 5, x ≥ 0D) g(x) = ✓x + 5, x ≥ -5

Answer 1

The given function is

`f(x)=(x-5)^2,x\ge5`

To find its inverse g(x) we will do these steps

1. Replace f(x) by y

`y=(x-5)^2`

2. Switch x and y

`x=(y-5)^2`

3. Solve to find y

Take a square root for both sides

`\begin{gathered} \sqrt[]{x}=\sqrt[]{(y-5)^2} \\ \sqrt[]{x}=y-5 \end{gathered}`

Add 5 to both sides

`\begin{gathered} \sqrt[]{x}+5=y-5+5 \\ \sqrt[]{x}+5=y \end{gathered}`

4. Replace y by g(x)

`g(x)=\sqrt[]{x}+5,x\ge0`

The answer is the 3rd choice