Question

What is the inverse function for f(x)= square root of 1/2x+4

Answer 1

The inverse of f(x) would be f(x) = 2$x^{2}$ - 8.

We can find this by taking the original equation and switching the x and f(x). Once we do this, we solve for the f(x) in its new place and that is the inverse equation. It is taken step by step for you below.

Take the original.

f(x) = $\sqrt{\frac{1}{2}x + 4}$

Now switch the x and f(x)

x = $\sqrt{\frac{1}{2}f(x) + 4}$

Now square both sides.

$x^{2}$ = $\frac{1}{2}$f(x) + 4

Now subtract 4 from both sides.

$x^{2}$ - 4 = $\frac{1}{2}$f(x)

Now multiply both sides by 2.

2$x^{2}$ - 8 = f(x)

And once you've returned to f(x) =, then you have your inverse.

Answer 2

The final answer is f(x) = 2 x^{2} - 8.