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gayaneshka [121]
3 years ago
15

2. Which of the functions below is an inverse of the quadratic function f(x) = x2 - 3 ?

Mathematics
1 answer:
mezya [45]3 years ago
3 0

Answer:

the inverse of the quadratic function f(x) = x^2 - 3  is \mathbf{f^{-1}(x)=\pm \sqrt{x+3}}

Step-by-step explanation:

We need to find inverse of the quadratic function f(x) = x^2 - 3

Let

y=x^2-3

Replace x and y

x=y^2-3

Now, we will solve for y

Adding 3 on both sides

x+3=y^2-3+3

x+3=y^2

Taking square root on both sides

\sqrt{y^2}=\sqrt{x+3}\\y=\pm \sqrt{x+3}

Now replace y with f^{-1}(x)

f^{-1}(x)=\pm \sqrt{x+3}

So, the inverse of the quadratic function f(x) = x^2 - 3  is \mathbf{f^{-1}(x)=\pm \sqrt{x+3}}

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