The inverse of the function 𝑓(𝑥)=1−4𝑥5 is the function

To find the inverse of the function f(x) = 1 - 4x^5, we need to follow these steps:

1. Replace f(x) with y. This gives us y = 1 - 4x^5.

2. Swap x and y. This gives us x = 1 - 4y^5.

3. Solve for y. This is a bit tricky because y is inside a power of 5.

First, isolate the term with y by subtracting 1 from both sides: x - 1 = -4y^5.

Then, divide both sides by -4 to solve for y^5: (x - 1) / -4 = y^5.

Finally, take the fifth root of both sides to solve for y. The fifth root of a number is the same as raising that number to the power of 1/5. So, y = [(x - 1) / -4]^(1/5).

So, the inverse of the function f(x) = 1 - 4x^5 is y = [(x - 1) / -4]^(1/5).