ACT Math · Function notation and transformations
If f(x) = x + 2 and g(x) = x - 2, what is (f · g)(5)?
If and , what is ?
Answer and explanation
Answer: B: 21
The notation means the product . Compute and . The product is , choice B. Using the product function, , and at that is . Choice A () adds and , which is . Choice C () is , forgetting the . Choice D () is alone. A dot between functions means multiplication of their outputs. The two methods agree, so the answer is reliable.
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)?
Learn the method behind questions like this one
The ACT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.