Respuesta :

ponytail151

Answer:

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

Step-by-step 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

Happil

Writing a function in its inverse form

Answer:

[tex]f^{-1}(x) = \frac{1}{5}x\\[/tex]

Step-by-step explanation:

Given:

[tex]f(x) = 5x[/tex]

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

[tex]x = 5y \\ 5y = x \\ 5y \times \frac{1}{5} = x \times \frac{1}{5} \\ y = \frac{1}{5}x[/tex]

Since [tex]y[/tex] is [tex]f(x)[/tex], the inverse of [tex]y[/tex] should be the inverse of [tex]f(x)[/tex] or it is [tex]f^{-1}(x)[/tex]

We can then substitute inverse [tex]y[/tex] with [tex]f^{-1}(x)[/tex]

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