Question

Which represents the inverse of the function f(x) = 4x?

h(x) = x + 4
h(x) = x – 4
h(x) = three-quartersx
h(x) = one-quarterx

Answer 1

h(x) = one-quarter is the correct answer!

Answer 2

By definition, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= $\frac{1}{4}$x.

Definition of inverse function

The inverse or reciprocal function of f(x) is called another function f⁻¹(x) that satisfies: If f(x)=y , then f⁻¹(y)=x.

To build or calculate the inverse function of any function, one of the ways to do it is to interchange the variables x and y, and use a combination of algebraic methods in order to isolate the variable "y".

Inverse of f(x)=4x

Being f(x)=y=4x, to calculate the inverse, in first place you interchange the variables x and y:

f(y)=x=4y

Isolating the variable y, you get:

h(x)=x÷4= $\frac{1}{4}$x

Finally, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= $\frac{1}{4}$x.

Learn more about the inverse of a function:

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