If f of x is equal to the fraction with numerator x minus 6 and denominator x , g of x is equal to x plus 4 , and h of x is equal to 3 x minus 2 , what is open paren h circ f circ g close paren times x ?
Answer
A
open paren h circ f circ g close paren times x is equal to the fraction with numerator 3 x minus 4 and denominator x
B
open paren h circ f circ g close paren times x is equal to the fraction with numerator x minus 2 and denominator x plus 4
C
open paren h circ f circ g close paren times x is equal to the fraction with numerator 3 x minus 8 and denominator x
D
open paren h circ f circ g close paren times x is equal to the fraction with numerator x minus 14 and denominator x plus 4
Explanation
Apply the functions from the inside out. First, g(x) = x + 4, so f(g(x)) = ((x + 4) − 6)/(x + 4) = (x − 2)/(x + 4). Then h(f(g(x))) = 3(x − 2)/(x + 4) − 2 = (x − 14)/(x + 4), which matches choice D.
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