If h(x)=x2−2xandg(x)=3x+5, then what (h⋅g)(−4)?

1 Answer
Ben
May 30, 2018

Should be -168

Explanation:

Assuming that (h⋅g)(x)=h(x)⋅g(x), we can either evaluate both functions separately and then multiply together, or we can combine the functions and then solve. Let's do the latter first, then the former:

(h⋅g)(x)=(x2−2x)(3x+5)

(h⋅g)(x)=3x3+5x2−6x2−10x

(h⋅g)(x)=3x3−x2−10x

Now, solve the function for x=−4

(h⋅g)(−4)=3(−4)3−(−4)2−10(−4)

(h⋅g)(−4)=3(−64)−16+40

(h⋅g)(−4)=−192−16+40

(h⋅g)(−4)=−168

Let's try solving each function separately, then combining:

h(−4)=(−4)2−2(−4)

h(−4)=16+8=24

g(−4)=3(−4)+5

g(−4)=−12+5=−7

h(−4)⋅g(−4)=(h⋅g)(−4)=24⋅(−7)

(h⋅g)(−4)=−168

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