Question

What is the inverse of the function f (x) = 3(x + 5)2 – 4, such that x ≤ –5?

Answer 1

The inverse of function f(x) = 3(x + 5)² - 4 is given by:

$f^{-1}(x) = -5 - \sqrt{\frac{x + 4}{3}}$

How to find the inverse of a function f(x)?

To find the inverse of a function y = f(x), we exchange x and y and then isolate y.

In this problem, the function is:

y = 3(x + 5)² - 4.

Exchanging x and y, we have that:

x = 3(y + 5)² - 4

Now we work to isolate y.

$3(y + 5)^2 = x + 4$

$(y + 5)^2 = \frac{x + 4}{3}$

$y + 5 = \pm \sqrt{\frac{x + 4}{3}}$

We have x ≤ –5, hence we take the negative value of the root, as follows:

$y + 5 = -\sqrt{\frac{x + 4}{3}}$

$y = -\sqrt{\frac{x + 4}{3}} - 5$

Hence the inverse function is given by:

$f^{-1}(x) = -5 - \sqrt{\frac{x + 4}{3}}$

More can be learned about the inverse of a function at brainly.com/question/25897382

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