SAT Math: Function Composition
20+ practice questions in Praczo
The concept, explained
- 1
Function composition f(g(x)) means applying function g first, then taking its output and plugging it into function f.
- 2
Work from the inside out: for f(g(3)), find g(3) first. If g(3) = 5, then find f(5).
- 3
When composing algebraically, substitute the entire expression for g(x) everywhere there is an x in f(x).
- 4
f(g(x)) is rarely equal to g(f(x)). The order matters significantly.
- 5
On graphs or tables, locate the inner function's value on the y-axis (or output column), then use that as the input (x-value) for the outer function.
- ✗ Multiplying f(x) and g(x) together instead of substituting one into the other.
- ✗ Evaluating the outer function first instead of the inner function.
SAT-style practice
If f(x) = 2x + 1 and g(x) = x², what is the value of f(g(3))?
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