which of the following is the correct representation of ( h(x) = f(x) + g(x) ) when ( f(x) = 4x^2 - x + 3 )…

which of the following is the correct representation of ( h(x) = f(x) + g(x) ) when ( f(x) = 4x^2 - x + 3 ) and ( g(x) = -2x^2 + 5x - 1 )?\n\na. ( h(x) = -6x^2 + 6x - 4 )\nb. ( h(x) = 6x^2 - 4x + 4 )\nc. ( h(x) = 2x^2 + 4x + 2 )\nd. ( h(x) = 2x^2 + 6x - 4 )

which of the following is the correct representation of ( h(x) = f(x) + g(x) ) when ( f(x) = 4x^2 - x + 3 ) and ( g(x) = -2x^2 + 5x - 1 )?\n\na. ( h(x) = -6x^2 + 6x - 4 )\nb. ( h(x) = 6x^2 - 4x + 4 )\nc. ( h(x) = 2x^2 + 4x + 2 )\nd. ( h(x) = 2x^2 + 6x - 4 )

Answer

Answer:

c. $h(x) = 2x^2 + 4x + 2$

Explanation:

Step1: Define $h(x)$ as sum

$h(x) = f(x) + g(x)$

Step2: Substitute given functions

$h(x) = (4x^2 - x + 3) + (-2x^2 + 5x - 1)$

Step3: Combine like $x^2$ terms

$4x^2 - 2x^2 = 2x^2$

Step4: Combine like $x$ terms

$-x + 5x = 4x$

Step5: Combine constant terms

$3 - 1 = 2$

Step6: Assemble final $h(x)$

$h(x) = 2x^2 + 4x + 2$