Answer:
fourth option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 4x ( divide both sides by 4 )
[tex]\frac{y}{4}[/tex] = x
Change y back into terms of x with x as the inverse function, thus
h(x) = [tex]\frac{x}{4}[/tex] = [tex]\frac{1}{4}[/tex] x
Answer:
h(x)=1/4x
Step-by-step explanation:
To find the inverse of a function, switch the "x" and the "y". The f(x) can be considered as "y".
[tex]f(x)=4x[/tex]
[tex]y=4x[/tex]
[tex]x=4y[/tex]
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.
[tex]\frac{x}{4} =\frac{4y}{4}[/tex]
[tex]\frac{x}{4} =y[/tex]
x/4 can be rewritten as 1/4x.
[tex]y=\frac{1}{4} x[/tex]
[tex]h(x)=\frac{1}{4} x[/tex]
The inverse of the function f(x)=4x is h(x)=1/4x
