Question

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

h(x)=x+4
h(x)=x-4
h(x)=3/4x
h(x)=1/4x

Answer 1

fourth option

Explanation:

let y = f(x) and rearrange making x the subject, that is

y = 4x ( divide both sides by 4 )

`(y)/(4)` = x

Change y back into terms of x with x as the inverse function, thus

h(x) =
`(x)/(4)` =
`(1)/(4)` x

Answer 2

h(x)=1/4x

Explanation:

To find the inverse of a function, switch the "x" and the "y". The f(x) can be considered as "y".

`f(x)=4x`

`y=4x`

`x=4y`

We want to isolate y. 4 and y are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 4.

`(x)/(4) =(4y)/(4)`

`(x)/(4) =y`

x/4 can be rewritten as 1/4x.

`y=(1)/(4) x`

`h(x)=(1)/(4) x`

The inverse of the function f(x)=4x is h(x)=1/4x