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Ksivusya [100]
2 years ago
14

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

Mathematics
1 answer:
yuradex [85]2 years ago
3 0

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

<h3>How to determine the inverse function?</h3>

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

Read more about inverse function at:

brainly.com/question/2541698

#SPJ1

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