Question

Find the inverse of f(x)=5x^3

Answer 1

Replace f(x) with y. We get y=5x^3.

Swap x and y. We get x=5y^3.

Solve for y. We get y=(x/5)^(1/3).

Change y to f-1(x). We get f-1(x)=(x/5)^(1/3).

Therefore, the inverse of f(x)=5x^3 is f-1(x)=(x/5)^(1/3).

I don't if this is enough or not but this is what I get.

Answer 2

the inverse of f(x) = 5x^3 is g(x) = (x/5)^(1/3).

Explanation:

To find the inverse of f(x) = 5x^3, we need to find a function g(x) such that g(f(x)) = x.

Let y = f(x) = 5x^3, then we solve for x in terms of y:

y = 5x^3

x^3 = y/5

x = (y/5)^(1/3)

Thus, g(x) = (x/5)^(1/3).

Therefore, the inverse of f(x) = 5x^3 is g(x) = (x/5)^(1/3).