Mathematics: 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.

Consider the function y = 9 - x2, where x ≥ 3. what

Ответ:

aedmund1225

30.12.2021

Mathematics

$y^{-1}=\sqrt{9-x}\qquad where\ x\leq 9$

Step-by-step explanation:

Given that y = 9 - x² where x ≥ 3 ⇒ y ≥ 0

To find the inverse, swap the x's and y's and solve for y inverse (y⁻¹)

$y = 9 - x^2\\\\x = 9 - (y^{-1})^2\\\\(y^{-1})^2 = 9 - x\\\\\sqrt{(y^{-1})^2} = \sqrt{9 - x}\\\\y^{-1}=\pm\sqrt{9-x}\qquad \text{Since y}\geq 0, \text{then the negative is not valid}\\\\y^{-1}=\sqrt{9-x}$

The domain is the restriction on the x-values of the equation. Since the radicand (term under the square root symbol) must be greater than or equal to 0, then

9 - x ≥ 0

9 ≥ x ⇒ x ≤ 9

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Ответ:

crobinson5087

17.08.2021

Mathematics

An algebraic expression is a mathematical expression that consists of variables, numbers, and operations. We can use algebraic expressions to represent unknown number situations involving addition, subtraction, multiplication, and division.

Step-by-step explanation:

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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.

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