f(g(2)) means work g(2) first, then feed its answer into f. These free printable worksheets compose two functions and evaluate them, inside rule first.
Composition adds the one reliable mistake to function notation: working the outside first. f(g(2)) is read left to right and worked right to left — find g(2), then put that number into f. Choosing which rule is inside is what a test actually asks, and it is the whole of what this sheet drills.
Why this sheet works
The arithmetic is kept light on purpose so the order is what shows. Every rule is a straight line and every answer is a whole number, so a child is never fighting heavy computation while also tracking which function goes first. What is being practiced is the reading and the sequence, not the sums.
How this one works
One question from this sheet, worked through a step at a time.
f(x) = x, g(x) = −3x + 3; f(g(6))
f(x) = x
g(x) = −3x + 3
g(6)=−15
f(−15)=−15
f(g(6))=−15
f(g(6)) means work the inside first: find g(6), then put THAT answer into f.
