If s times x is equal to x minus 7 and t times x is equal to 4 x squared minus x plus 3 , which expression is equivalent to open paren t circ s close paren times x ?
Answer
A
4 times open paren x minus 7 close paren squared minus x minus 7 plus 3
B
open paren 4 x squared minus x plus 3 close paren minus 7
C
open paren 4 x squared minus x plus 3 close paren times open paren x minus 7 close paren
D
4 times open paren x minus 7 close paren squared minus open paren x minus 7 close paren plus 3
Explanation
The composition (t ∘ s)(x) means first apply s, then apply t: (t ∘ s)(x) = t(s(x)). Since s(x) = x − 7 and t(u) = 4u² − u + 3, substitute x − 7 for every input u in t to get 4(x − 7)² − (x − 7) + 3. This matches choice A.
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