Mathematics, 28.05.2021 08:40 dancekb2

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

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Answer from: mettababeeeee

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.

Answer from: Quest

- 1.613 = -1.6 or -1.61

-1.522 = -1.5 or -1.52

0.587 = 0.6 or 0.59

3.079 = 3.1 or 3.08

Answer from: Quest

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(continued on page 79)

step-by-step explanation:

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