Question

What is the inverse of this function? f(x)=-1/2 square root of x+3, x > -3

Answer 1

The inverse function of $f(x) = -\frac 12\sqrt{x + 3}$ is$f^{-1}(x) = 4x^2- 3$

How to determine the inverse function?

The function is given as:

$f(x) = -\frac 12\sqrt{x + 3}$

Rewrite as;

$y = -\frac 12\sqrt{x + 3}$

Swap the positions of x and y

$x = -\frac 12\sqrt{y + 3}$

Multiply through by -2

$-2x = \sqrt{y + 3}$

Square both sides

4x^2 = y + 3

Subtract 3 from both sides

y = 4x^2 - 3

Express as an inverse function

$f^{-1}(x) = 4x^2- 3$

Hence, the inverse function of $f(x) = -\frac 12\sqrt{x + 3}$ is$f^{-1}(x) = 4x^2- 3$

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