Which function is the inverse of f(x) = 1/4 x^3 + 1

A) F^-1(x)= 3 SR 4x
B) F^-1(x)=3 SR x-1
C) F^-1(x)= 3 SR 4x-4
D) F^-1(x)= 3 SR 4x-1

Question

Which function is the inverse of f(x) = 1/4 x^3 + 1

A)  F^-1(x)= 3 SR 4x
B)  F^-1(x)=3 SR x-1
C)  F^-1(x)= 3 SR 4x-4
D)  F^-1(x)= 3 SR 4x-1

anonymous · Answer

I have no idea what to do here. So if anyone could guide me through it I would greatly appreciate it.

anonymous · Answer

let f(x) = y first..

So:

$$\large y = \frac{1}{4}x^3 + 1$$

Right??

anonymous · Answer

Right.

anonymous · Answer

You must do the inverse operations in inverse order.
This equation is x cubed, then times 4 then plus 1.
So the inverse is: ...

anonymous · Answer

So:

$$y - 1 = \frac{1}{4} x^3$$

$$x^3 = 4y - 4 \implies x = \sqrt[3]{4y - 4}$$

Just swap x and y here

anonymous · Answer

replace  x by y and y with x here you will get  $f^{-1}(x)$..

anonymous · Answer

Welcome dear...