If h(x)=x22xandg(x)=3x+5, then what (hg)(4)?

1 Answer
May 30, 2018

Should be -168

Explanation:

Assuming that (hg)(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:

(hg)(x)=(x22x)(3x+5)

(hg)(x)=3x3+5x26x210x

(hg)(x)=3x3x210x

Now, solve the function for x=4

(hg)(4)=3(4)3(4)210(4)

(hg)(4)=3(64)16+40

(hg)(4)=19216+40

(hg)(4)=168

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

h(4)=(4)22(4)

h(4)=16+8=24

g(4)=3(4)+5

g(4)=12+5=7

h(4)g(4)=(hg)(4)=24(7)

(hg)(4)=168