If f of x is equal to the fraction with numerator x plus 4 and denominator x , g of x is equal to x minus 2 , and h of x is equal to 4 x minus 1 , what is open paren f circ h circ g close paren times x ?
Answer
A
open paren f circ h circ g close paren times x is equal to the fraction with numerator 2 x plus 16 and denominator x
B
open paren f circ h circ g close paren times x is equal to the fraction with numerator 2 x plus 4 and denominator x
C
open paren f circ h circ g close paren times x is equal to the fraction with numerator 4 x minus 3 and denominator 4 x minus 7
D
open paren f circ h circ g close paren times x is equal to the fraction with numerator 4 x minus 5 and denominator 4 x minus 9
Explanation
Apply the functions from right to left. First, g(x) = x − 2, then h(g(x)) = 4(x − 2) − 1 = 4x − 9. Since f(u) = (u + 4)/u, substitute u = 4x − 9 to get (f ∘ h ∘ g)(x) = (4x − 9 + 4)/(4x − 9) = (4x − 5)/(4x − 9), which is choice D.
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