For the given functions f and g , find the indicated composition.

Question

f(X) = 9x^2-4x, g(x) = 8x-3

(f.g)(5)

Answer 1

(f∘g)(5) = f(g(5))

g(5) = 8(5) - 3

= 40 - 3

= 37

f(37) = 9(37)^2 - 4(37)

= 9(1369) - 4(37)

= 12,321 - 148

= 12,173

Hence, (f∘g)(5) = 12,173

Answer 2

f(x) = 9x^2 -4x

g(x) = 8x-3

find f(g(x)) when x =5

g(5) = 8(5)-3 = 40-3 =37

f(g(5)) = 9(37^2 - 4(37) = 12321- 148 = 12,173

or f(g(x)) = 9(8x-3)^2 -4(8x-3) = 9(64x^2 -48x + 9) - 32x + 12 = 576x^2 -432x +81-32x+12=576x^2 -464x +93

then

f(g(5)) = 576(5^2) -464(5) + 93 = 576(25) - 2320 + 93 = 57600/4 - 2227 = 14400-2227 = 12266, OK slight mistake on 2nd method, but still very close arithmetic mistake in 2nd method

go with 1st method f(g(5)) = 12, 173