Find the inverse of the function. f(x) = the cube root of quantity x divided by seven -9?

Solution:

An inverse function is a function that undoes the action of another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

Given: Function f(x) = the cube root of quantity x divided by seven -9

It can be mathematically represented as

f(x) = ³√(x/7) - 9

Now replace f (x) with y

y = ³√ (x/7) - 9

As we have to determine the inverse we have to interchange the variables

x = ³√(y/7) - 9

By further simplification

x + 9 = ³√(y/7)

Cubing on both sides

(x + 9)³ = y/7

By cross multiplication

7(x + 9)³ = y

Now replace y with f^-1(x)

f^-1(x) = 7 (x + 9)³

Therefore, the inverse of the functions is 7(x + 9)³.

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Find the inverse of the function. f(x) = the cube root of quantity x divided by seven -9?

Summary:

The inverse of the function f(x) = the cube root of quantity x divided by seven -9 is 7(x + 9)³.