ACT Math · Function notation and transformations

If f(x) = 3x - 1 and g(x) = x² - 4, what is g(f(2))?

If f(x)=3x−1f(x) = 3x - 1 and g(x)=x2−4g(x) = x^2 - 4, what is g(f(2))g(f(2))?

Answer and explanation

Answer: J: 21

The notation g(f(2))g(f(2)) means apply ff first. f(2)=3(2)−1=5f(2)=3(2)-1=5. Then g(5)=52−4=21g(5)=5^2-4=21, choice J. Choice F (55) stops after the inner function and reports f(2)f(2). Choice G (00) is g(2)=22−4g(2)=2^2-4, which skips ff and uses 22 in gg directly. Choice H (1616) squares f(2)−1=4f(2)-1=4 instead of squaring 55, which does not follow the definition of gg. The inside function is always evaluated first, and its output becomes the input of the outside function.

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