ACT Math · Function notation and transformations

If f(x) = x + 2 and g(x) = x - 2, what is (f · g)(5)?

If f(x)=x+2f(x) = x + 2 and g(x)=x−2g(x) = x - 2, what is (f⋅g)(5)(f \cdot g)(5)?

Answer and explanation

Answer: B: 21

The notation (f⋅g)(5)(f\cdot g)(5) means the product f(5)⋅g(5)f(5)\cdot g(5). Compute f(5)=5+2=7f(5)=5+2=7 and g(5)=5−2=3g(5)=5-2=3. The product is 7⋅3=217\cdot3=21, choice B. Using the product function, (x+2)(x−2)=x2−4(x+2)(x-2)=x^2-4, and at x=5x=5 that is 25−4=2125-4=21. Choice A (1010) adds f(5)f(5) and g(5)g(5), which is (f+g)(5)(f+g)(5). Choice C (2525) is 525^2, forgetting the −4-4. Choice D (33) is g(5)g(5) alone. A dot between functions means multiplication of their outputs. The two methods agree, so the answer is reliable.

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