Question

Inverse of g(x)=-x^5-3

Answer 1

Answer:

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

Step-by-step explanation:

$g(x) = - {x}^{5} - 3$

To find the inverse of g(x) equate g(x) to y

That's

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

Next interchange the terms

x becomes y and y becomes x

We have

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

Next make y the subject

Multiply both sides by - 1

That's

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

Send 3 to the right side of the equation

That's

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

Find the 5th root of both sides

That's

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

We have the final answer as

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

Hope this helps you