Which expression represents the composition open bracket g circ f circ h close bracket times x for the functions? f of x is equal to 5 x minus 4 g of x is equal to 5 x cubed h of x is equal to 3 x
Answer
A
open paren 75 x minus 20 close paren cubed
B
5 times open paren 5 x minus 4 close paren cubed
C
5 times open paren 15 x minus 4 close paren cubed
D
675 x cubed minus 4
Explanation
Apply the functions from the inside out. First, h(x) = 3x, so f(h(x)) = 5(3x) − 4 = 15x − 4. Then g(f(h(x))) = 5(15x − 4)³, which matches choice C.
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