Question

Find the inverse of the function.

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

a f-1(x) = 21(x + 9)
b f-1(x) = [7(x + 9)]3
c f-1(x) = 7(x3 + 9)
d f-1(x) = 7(x + 9)3

Answer 1

The equation that is given in this item can be mathematically expressed as,
f(x) = (x/7)^(1/3) - 9

The expression f(x) can be replaced with y such that the equation can also be written as,
y = (x/7)^(1/3) - 9

The first thing that needs to be done to get the inverse of the function is to interchange the positions of x and y. In this equation, that becomes,
x = (y/7)^(1/3) - 9

Then, solve for the value of y in terms of x.
Transpose the constant to the other side of the equation.
x + 9 = (y/7)^(1/3)

Raise the whole equation by 3 in order to eliminate the radical.
(x+9)³ = (y/7)
Multiply the equation by 7 to eliminate the fraction.
(x+9)³(7) = y

Thus, the inverse of the function is equal to
f⁻¹(x) = 7(x+9)³

The answer is letter B.