Question

If f(x) = 5x, what is f–1(x)?

Answer 1

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

Explanation:

we have

`f(x)=5x`

Let

y=f(x)

`y=5x`

Exchange the variables x for y and y for x

`x=5y`

isolate the variable y

`y=x/5`

Let

`f^(-1) (x)=y`

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

Answer 2

Option c

Explanation:

Give that f(x) = 5x

We have to choose among the four options which is the inverse of f

Let us try directly from f(x)

`f(x) = 5xy =5x`

Divide both sides by 5

`x = (y)/(5) </p><p>Verify:</p><p>Let us do composiition of function as</p><p>\\[tex]f(f^(-1) (x))=f((1)/(5)x)\\ =5((1)/(5)x)\\\\=x`=\frac{1}{5} x[/tex]

WE find that our answer is right