Question

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

Answer 1

Answer:

Option B.

Step-by-step 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:

$f(x) = \sqrt{x} - 5$

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

Inverse function:

$y = \sqrt{x} - 5$

Exchanging x and y

$x = \sqrt{y} - 5$

$\sqrt{y} = x + 5$

$(\sqrt{y})^2 = (x+5)^2$

$y = (x+5)^2$

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.