9
QuizMultiple Choice

Composition of Functions — Quiz

Question 9 • Mathematics III

If p times x is equal to 2 x squared minus 4 x and q times x is equal to x minus 3 , what is open paren p circ q close paren times x ?

Answer
A
2 x squared minus 16 x plus 15
B
2 x squared minus 16 x plus 18
C
2 x squared minus 4 x plus 12
D
2 x squared minus 16 x plus 30

Explanation

To find (p ∘ q)(x), substitute q(x) = x − 3 into p(x) = 2x² − 4x. This gives 2(x − 3)² − 4(x − 3) = 2x² − 12x + 18 − 4x + 12 = 2x² − 16x + 30. The correct choice is C, 2x² − 16x + 30.

AI-written and checked against the verified answer.

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