Which expression represents the composition open bracket f circ g circ h close bracket times x for the functions? f of x is equal to negative 2 x to the 4th power g of x is equal to 4 x minus 6 h of x is equal to x minus 1
Answer
A
negative 2 times open paren 4 x minus 6 close paren to the 4th power minus 1
B
negative 8 times open paren x minus 1 close paren to the 4th power minus 6
C
negative 2 x to the 4th power minus 1
D
negative 2 times open paren 4 x minus 10 close paren to the 4th power
Explanation
For the composition f(g(h(x))), start with h(x)=x−1 and substitute it into g: g(h(x))=4(x−1)−6=4x−10. Then apply f(u)=−2u⁴ to get −2(4x−10)⁴, which is choice D.
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