Let 𝑓(𝑥) = 𝑚𝑥^2 + 2𝑥 + 5 and 𝑔(𝑥) = 2𝑥^2 − 𝑛𝑥 − 2. The functions are combined to form the new function ℎ(𝑥) = 𝑓(𝑥) × 𝑔(𝑥). Points (1, −40) and (−1, 24) satisfy the new function. Determine 𝑓(𝑥) and 𝑔(𝑥).
f(1) = m+2+5 = m+7
f(-1) = m-2+5 = m+3
g(1) = 2-n-2 = -n
g(-1) = 2+n-2 = n
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h(1) = (m+7)(-n) = -40
h(-1) = (m+3)(n) = 24
mn+7n = 40
mn+3n = 24
4n = 16
n = 4
so 4m+28=40 ==> m = 3
now finish it off and check your final answers.