How Do You Find The inverse function of g(x)=x^3,f(x)=1/8x-3?

We'll find the inverse of the function
f(x).

f(x)=1/(8x-3)

We'll note
f(x) as y, so, y = f(x) = 1/(8x-3)

Now, we'll multiply the
denominator (8x-3) by y:

y* (8x-3) =
1

We'll remove the
brackets:

8xy - 3y = 1

We'll
isolate y to the left side. For this reason, we'll add 3y both
sides:

8xy = 1 + 3y

We'll
divide by 8y both sides:

x =
(1+3y)/8y

The expression of the inverted function
is:

f(y) =
(1+3y)/8y

 Conventionally, a function has as variable x,
so, we'll re-write the inverse
function:

f^-1(x) =
(1+3x)/8x

To determine the inverse function
of g(x), we'll cover the same ground.

First, we'll note the
function g(x) = y.

g(x) = y =
x^3

We'll keep  y = x^3.

We'll
raise to the power (1/3) both sides:

 y^(1/3) =
x

The inverse function of g(x)
is:

g^-1(x) =
x^(1/3)