F(x)= square root of x-5. find f-1 (x) and it’s domain

Question

asked Jan 14, 2022 83.1k views

2 Answers

Ivan Nosov · Answer 1 · 2022-01-19T02:09:55+0000

Answer:

Option B.

Explanation:

Inverse function:

Suppose we have a function y = f(x). To find the inverse function, we exchange x and y on the original function, and then isolate y.

The domain of the inverse function(x values) is the range of the original function(y values).

Original function:

f(x) = √(x) - 5

Domain is
$[0,\infty)$ , and when
x = 0, f(x) = -5 . So the range is
$[-5,\infty]$ , that is,
$y \geq -5$

Inverse function:

y = √(x) - 5

Exchanging x and y

x = √(y) - 5

√(y) = x + 5

(√(y))^2 = (x+5)^2

y = (x+5)^2

The inverse function is
f^(-1)(x) = (x+5)^2

Domain:

Range of the original function is
$y \geq -5$ , so the domain of the inverse function is
$x \geq -5$ . The correct answer is given by option B.