Getting the order wrong in composite functions H
"The Order Flip"
The Mistake in Action
Given $f(x) = x + 3$ and $g(x) = 2x$. Find $fg(4)$.
Wrong: $fg(4) = f(4) \times g(4) = 7 \times 8 = 56$
Why It Happens
Students interpret $fg(x)$ as "f times g" rather than "f of g" — a composition.
The Fix
$fg(x)$ means $f(g(x))$ — apply $g$ first, then $f$.
Read from right to left: $fg(4)$ = f of (g of 4)
Step 1: Find $g(4)$ $$g(4) = 2 \times 4 = 8$$
Step 2: Find $f(8)$ $$f(8) = 8 + 3 = 11$$
So $fg(4) = 11$
Not: $f(4) \times g(4)$ — that would be written as $f(4) \cdot g(4)$
Spot the Mistake
Can you identify where this student went wrong?
$fg(4)$
$= f(4) \times g(4) = 56$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: