Question

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

Answer 1

Given function: $f(x)=-4\sqrt{x}-1$.

We need to find the inverse of the given function f(x).

Let us write the function in terms of x and y first.

$y=-4\sqrt{x}-1$

Now, in order to find the inverse, we need to switch x and y, we get

$x=-4\sqrt{y}-1$

Now, we need to solve it for y.

In order to solve it for y, we need to isolate it for y.

Adding 1 on both sides, we get

$x+1=-4\sqrt{y}-1+1$

$x+1=-4\sqrt{y}$

Dividing both sides by -4, we get

$\frac{x+1}{-4}=\sqrt{y}$

In order to get rid square root from right side, we need to square both side.

$(\frac{x+1}{-4})^2=(\sqrt{y})^2$

$\frac{(x+1)^2}{16}=y$

Or $y=\frac{1}{16}(x+1)^2$

Therefore, inverse function is

$f^{-1}(x)=\frac{1}{16}(x+1)^2$.