Question

Given the function f(x) = x^2-13, _> 0, complete part A, B, and C

Answer 1

(a)

`f^(-1)(x)=\sqrt[]{x+13},\text{ }x\ge-13`

(c) The domain and range of f(x) are:

Domain is [0, ∞) and the range is [-13, ∞)

The domain and range of f⁻¹(x) are:

Domain is [-13, ∞) and the range is [0, ∞)

Step-by-step explanation

Given function:

`f(x)=x^2-13,x\ge0`

(a) To find f⁻¹(x)

Let y = f(x)

This implies

`\begin{gathered} y=x^2-13 \\ y+13=x^2 \\ x^2=y+13 \\ x=\sqrt[]{y+13} \\ \text{Note that x }=f^(-1)(y) \\ f^(-1)(y)=\sqrt[]{y+13} \\ \therefore f^(-1)(x)=\sqrt[]{x+13},\text{ }x\ge-13 \end{gathered}`

(c) The domain and range of f(x) are:

Domain is [0, ∞) and the range is [-13, ∞)

The domain and range of f⁻¹(x) are:

Domain is [-13, ∞) and the range is [0, ∞)