Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Functions
A function takes an input and gives one output. f(3) means "put 3 in for x." Composite functions work from the inside out.
- Replace every x in the rule with the input, in parentheses.
- For f(g(x)), find g first, then put that result into f.
- For a table or graph, read the output for the given input. f(a) = b means the point (a, b).
- When the choices are expressions, plug in a simple number. Pick x = 2, work out the answer the question wants, then test each choice with x = 2. Only the right one matches.
Q. f(x) = 2x + 3 and g(x) = x². What is f(g(2))?
Answer 11
g(2) = 4, then f(4) = 2(4) + 3 = 11. Note g(f(2)) = g(7) = 49, a different answer.
- Doing the outside function first.
- Squaring a negative input without parentheses: if f(x) = x², f(−3) = 9, not −9.
Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.