Question

Please help!

For the function f(x) -4 sqrtx - 1, find the inverse function.

Answer 1

1. B

2.D

3.B

4.A

Explanation:

Your Welcome

Answer 2

`f^-^1(x)=((x+1)^2)/(16)`

Explanation:

We have the function:
`f(x)=-4√(x) -1` and we have to find the inverse.

Observation:
`y=f(x)`, then
`y=-4√(x) -1`

You can obtain the inverse of a function by switching the x and y values. This means:

`y=-4√(x) -1\\x=-4√(y') -1`

We're going to call
`f^-^1(x)=y'`. Now we have to clear "y'".

First we have to add (1) in both sides of the equation:

`x=-4√(y') -1\\x+1=-4√(y')-1+1\\x+1=-4√(y')`

Now divide in (-4) both sides.

`x+1=-4√(y')\\((x+1))/((-4)) =((-4)√(y'))/((-4)) \\\\((x+1))/((-4)) =√(y')`

And for our last step we have to square both sides:

`((x+1))/((-4)) =√(y')\\\\(((x+1))/((-4)))^2=(√(y'))^2\\((x+1)^2)/((-4)^2)=y'\\\\((x+1)^2)/(16)=y'`

Then the third option is the correct:
`f^-^1(x)=((x+1)^2)/(16)`