Question

If g(x)= x^2-2x-6 and h(x)= 2x^2-5x+2 find (h-g) (-2)

Answer 1

`(h - g)( - 2) = 18`

Explanation:

g(x) = x² - 2x - 6

h(x) = 2x² - 5x + 2

To find (h-g) (-2) we must first find h - g(x)

To find h - g(x) subtract g(x) from h(x)

We have

`(h - g)(x) = {2x}^(2) - 5x + 2 - ( {x}^(2) - 2x - 6) \\ = {2x}^(2) - 5x + 2 - {x}^(2) + 2x + 6 \\ = {2x}^(2) - {x}^(2) - 5x + 2x + 2 + 6`

`(h - g)(x) = {x}^(2) - 3x + 8`

To find (h-g) (-2) substitute the value of x that's - 2 into (h - g)(x) that's replace every x in (h - g)(x) by - 2

That's

`(h - g)( - 2) = ({ - 2})^(2) - 3( - 2) + 8 \\ = 4 + 6 + 8 \\ = 10 + 8`

We have the final answer as

`(h - g)( - 2) = 18`

Hope this helps you