Question

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


Need help pls

Answer 1

Writing a function in its inverse form

Answer:

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

Explanation:

Given:

`f(x) = 5x`

Let
`y = f(x)` so we'll have the equation,
`y = 5x`. We then write it in its inverse form where we switch the
`x` and
`y`. The equation will be
`x = 5y`. Now we can solve for inverse
`y`.

`x = 5y \\ 5y = x \\ 5y * (1)/(5) = x * (1)/(5) \\ y = (1)/(5)x`

Since
`y` is
`f(x)`, the inverse of
`y` should be the inverse of
`f(x)` or it is
`f^(-1)(x)`

We can then substitute inverse
`y` with
`f^(-1)(x)`

Answer 2

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

Explanation:

For Inverse graphs, you interchange the x-values and the y-values.

Y=5x

Inverse:

x=5y (interchange x and y)

Change the values again, you'll get something like this -5y=-x

Divide both sides of the equation by -5

You'll get y = -x/-5

Using laws of exponents x/5 can be written as 1/5x

So y=1/5x