1 February, 19:26
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.
1 February, 20:04
Hello from MrBillDoesMath!
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
1 February, 21:20
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
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» 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.