Answer:
[tex]{f}^{ - 1} (x) = \sqrt[3]{x - 5} [/tex]
Step-by-step explanation:
[tex]f(x) = {x}^{3} + 5[/tex]
To find the inverse of f (x) , equate f(x) to y
That's
y = f(x)
[tex]y = {x}^{3} + 5[/tex]
Next interchange the terms
That's x becomes y and y becomes x
[tex]x = {y}^{3} + 5[/tex]
Next solve for y
Send 5 to the other side of the equation
[tex] {y}^{3} = x - 5[/tex]
Find the cube root of both sides to make y stand alone
That's
[tex] \sqrt[3]{ {y}^{3} } = \sqrt[3]{x - 5} [/tex]
[tex]y = \sqrt[3]{x - 5} [/tex]
We have the final answer as
[tex] {f}^{ - 1} (x) = \sqrt[3]{x - 5} [/tex]
Hope this helps you
