Question

If f(x)=5x, what is f^-1(x)?

Answer 1

Hello!

The answer is:

`f^(-1)(x)=(x)/(5)`

Why?

To invert a function we need to rewrite the variable with "y" and then, rewrite the function "f(x)" or "y" with x, and then, isolate "y".

Inverse functions means inversing the domain and the range from a function.

The given function is:

`f(x)=5x\\y=5x`

So, finding the inverse of the given function, we have:

`y=5x\\x=5y\\y=(x)/(5)`

Hence,

`f^(-1)(x)=(x)/(5)`

Have a nice day!

Answer 2

The inverse function f^-1 (x) = (1/5) x

Explanation:

* Lets explain what is the meaning of f^-1(x)

- f^-1 (x) the inverse function of f(x)

* How to find the inverse function

- In the function f(x) = ax + b, where a and b are constant

- Lets switch x and y

∵ y = ax + b

∴ x = ay + b

* Now lets solve to find y in terms of x

∵ x = ay + b ⇒ subtract b from the both sides

∴ x - b = ay ⇒ divide the two sides by a

∴ (x - b)/a = y

∴ The inverse function f^-1 (x) = (x - b)/a

* Lets do that with our problem

∵ f(x) = 5x ⇒ y = 5x

∴ x = 5y

- Find y in terms of x

∵ x = 5y ⇒ divide the both sides by 5

∴ x/5 = y

∴ f^-1 (x) = (1/5) x

* The inverse function f^-1 (x) = (1/5) x