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drek231 [11]
3 years ago
7

Consider the function y = 9 - x2, where x ≥ 3. What is the inverse of the function? What is the domain of the inverse? Show all

of your work for full credit.

Mathematics
2 answers:
lesya692 [45]3 years ago
7 0

Answer:

The inverse of the function is y^{-1}=\sqrt{9-x}.

The domain of the inverse function is D:(-\infty,0],\{x|x\in \mathbb{R}\}

Step-by-step explanation:

Given : Function y=9-x^2 where, x\geq 3

To find : What is the inverse of the function? What is the domain of the inverse?

Solution :

Function y=9-x^2

To find the inverse we interchange the value of x and y,

x=9-y^2

Now, we get the value of y

y^2=9-x

y=\pm\sqrt{9-x}

As x\geq 3 so x>0

y=\sqrt{9-x}

The inverse of the function is y^{-1}=\sqrt{9-x}.

The domain of the inverse is the range of the original function.

The range is defined as the set of all possible value of y.

As x\geq 3

Squaring both side,

x^2\geq 9

Subtract x^2 both side,

9-x^2\leq 0

y\leq 0

The range of the function is R:(-\infty,0],\{y|y\in \mathbb{R}\}

The domain of the inverse function is D:(-\infty,0],\{x|x\in \mathbb{R}\}

Brilliant_brown [7]3 years ago
5 0
Hello,
Please see the attached file.
Thanks.

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