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.

Question

asked Sep 11, 2019 217k views

2 Answers

Rachel Fishbein · Answer 1 · 2019-09-14T19:40:43+0000

Answer:

The inverse of the function is
y^(-1)=√(9-x) .

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

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

$y=\pm√(9-x)$

As
$x\geq 3$ so x>0

y=√(9-x)

The inverse of the function is
y^(-1)=√(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
$D:(-\infty,0],\{x|x\in \mathbb{R}\}$