Question

Find the inverse of the function f(x) = x3 + 5

Answer 1

Answer:

${f}^{ - 1} (x) = \sqrt[3]{x - 5}$

Step-by-step explanation:

$f(x) = {x}^{3} + 5$

To find the inverse of f (x) , equate f(x) to y

That's

y = f(x)

$y = {x}^{3} + 5$

Next interchange the terms

That's x becomes y and y becomes x

$x = {y}^{3} + 5$

Next solve for y

Send 5 to the other side of the equation

${y}^{3} = x - 5$

Find the cube root of both sides to make y stand alone

That's

$\sqrt[3]{ {y}^{3} } = \sqrt[3]{x - 5}$

$y = \sqrt[3]{x - 5}$

We have the final answer as

${f}^{ - 1} (x) = \sqrt[3]{x - 5}$

Hope this helps you