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

f(x) = 4x

le h(x) be the inverse

=> f(h(x)) = 4h(x)

=> x = 4h(x)

=> h(x) = x/4

Answer 2

Option D: $h(x)=\frac{1}{4}x$ is the inverse of the function

Explanation:

Given that the function $f(x)=4 x$

We need to determine the inverse of the function.

The inverse of the function can be determined by interchanging the variables of x and y and then, we shall solve the equation for y.

Thus, the function $f(x)=4 x$ can be written as

$y=4x$

Interchanging the variables, we get,

$x=4y$

Solving for y, we have,

$\frac{1}{4}x=y$

Thus, the inverse of the function is $h(x)=\frac{1}{4}x$

Hence, Option D is the correct answer.

Learn more:

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(2) If f(x) = 7x+12, what is the inverse function of f(x) equal to ?

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