Question

Which of the following is the inverse of f(x) = 3 − x⁵?

a. f−1(x) = 3 − 5x
b. f−1(x) = 5x − 3
c. f−1(x) = 5 x³
d. f−1(x) = 3 − x⁵

Answer 1

None of the provided options match this correct form. The concept of an inverse operation frequently applies to powers and roots in mathematics.

Step-by-step explanation:

The inverse of the function f(x) = 3 - x5 is found by replacing f(x) with y, switching the roles of x and y, and then solving for y. This yields:

• y = 3 - x5
• x = 3 - y5
• y5 = 3 - x
• y = (3 - x)1/5

The correct option is not explicitly listed, so the closest correct form of the inverse would be f-1(x) = (3 - x)1/5. But out of the given options, none are the precise inverse of the function f(x).

To address example A.8, the negative exponent rule states that an expression like x-n is equivalent to 1/xn. Thus, 3-4 is the same as 1/34.

Finding an inverse function relates to the overall concept of performing an inverse operation such as taking powers to roots, and here specifically it means solving for the variable of interest after swapping the dependent and independent variables.