Question

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Answer 1

Finding the inverse function of $f(x) = 5\sqrt{x + 3} - 2$, it is best described by graph B.

How to find the inverse of a function?

Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.

In this problem, the function is:

$f(x) = 5\sqrt{x + 3} - 2$

$y = 5\sqrt{x + 3} - 2$

Exchanging x and y:

$x = 5\sqrt{y + 3} - 2$

Working through the function to isolate y:

$5\sqrt{y + 3} = x + 2$

$\sqrt{y + 3} = \frac{x + 2}{5}$

$(\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2$

$y + 3 = \frac{(x + 2)^2}{25}$

$y = \frac{(x + 2)^2}{25} - 3$

$f^{-1}(x) = \frac{(x + 2)^2}{25} - 3$

Which is best represented by graph B.

More can be learned about inverse functions at brainly.com/question/27830327

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