Question

Consider the given functions.

f(x) = -5x^2 + 2x - 6

g(x) = -5x^2 -4x + 8

h(x) = 6x - 14



Select the expression that will produce h(x).

A. f(x) − g(x)
B. f(x) + f(x)
C. g(x) − f(x)
D. f(x) + g(x)

Only one answer.

Answer 1

Hello from MrBillDoesMath!

Answer: A

Discussion :

Note that h(x) does not contains an x^2 term where both f(x) and g(x) do. This means we need to subtract f(x) and g(x) to remove the x^2 term. The only choices are A and C but for C:

g(x) = -5x^2 - 4x + 8

-f(x) = 5x^2 - 2x + 6

Adding these terms gives

(-5x^2 + 5x^2) - 4x - 2x + (8 +6 ) =

0 - 6x + 14

which is NOT h(x). (It actually equals - h(x)) .

The only candidate is choice A

Regards, MrB

Answer 2

neat

in h(x) we notice that there are no x^2 terms,

we also notice that in f(x), the coeffent of the x^2 term is -5

in g(x), the coeffient of the x^2 term is also -5

in order to eliminate the x^2 terms, we must subtract one from another (since -5-(-5)=0), so the operation must be either f(x)-g(x) or g(x)-f(x)

we then can consider the constant term or the constant

if we look at the constant of h(x), we see that it is -14

in f(x) the constant is -6

in g(x) the constant is 8

we note that 14=-6-8, so g(x) must be multiplied by -1 then added to f(x)

ie f(x)-g(x)

if we check the linear term

in f(x), the linear term is 2x

in g(x) the linear term is -4x

if we do f(x)-g(x), the linear term will be 2x-(-4x)=2x+4x=6x which checks

the operation is f(x)-g(x)

answer is A