ACT Math · Function notation and transformations
If f(x) = 3x - 1 and g(x) = x² - 4, what is g(f(2))?
If and , what is ?
Answer and explanation
Answer: J: 21
The notation means apply first. . Then , choice J. Choice F () stops after the inner function and reports . Choice G () is , which skips and uses in directly. Choice H () squares instead of squaring , which does not follow the definition of . The inside function is always evaluated first, and its output becomes the input of the outside function.
More Function notation and transformations questions
- Question 15If f(x) = 2x - 3 and g(x) = x² + 1, what is f(g(2))?
- Question 17If f(x) = x² and g(x) = f(x-3) + 2, what is g(5)?
- Question 18A function is defined as f(x) = 2x+1 if x < 2, and f(x) = x²-3 if x ≥ 2. What is f(2) + f(-1)?
- Question 19If f(x) = (3x-5)/(2), what is f^-1(7)?
- Question 20The function f(x) = -2(x-3)² + 7 has its vertex at (3, 7). What is f(5)?
- Question 55A function is defined by the table below. If the pattern continues, what is f(6)?
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