Question

The amount of energy a microwave oven uses (in the form of electricity) is given by the function f(x)=5x+9, where x is the amount of time the microwave is turned on. The amount of energy the microwave puts out is modeled by the function g(x)=−x^2+3x+1, where x is the amount of time the microwave is turned on.

What is the difference between the amount of energy the microwave uses and the amount it puts out?

(x)=x^2+2x+8

f(x)=−x^2−2x−8

f(x)=−x^2+8x+10

f(x)=x^2−8x−10

Answer 1

The difference between the amount of energy the microwave uses and the amount it puts out is x² + 2x + 8 ⇒ first answer

Explanation:

* Lets explain how to solve the problem

- The amount of energy a microwave oven uses is given by the

function f(x) = 5x + 9

- The amount of energy the microwave puts out is given by the

function g(x) = − x² + 3x + 1

- x is the amount of time the microwave is turned on in

both functions

- To find the difference between the amount of energy the

microwave uses and the amount it puts out we will subtract

g(x) from f(x)

* Lets do that

∵ f(x) = 5x + 9

∵ g(x) = - x² + 3x + 1

∴ The difference = 5x + 9 - (-x² + 3x + 1) ⇒ multiply the bracket by (-)

- Remember that (-)(-) = (+) and (-)(+) = (-)

∴ The difference = 5x + 9 + x² - 3x - 1 ⇒ Add the like terms

∴ The difference = x² + (5x - 3x) + (9 - 1)

∴ The difference = x² + 2x + 8

* The difference between the amount of energy the microwave uses

and the amount it puts out is x² + 2x + 8