Find the inverse of the function.

1 answer:

3 0

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.

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