Composition & Inverses
Work from the inside out for composition, and swap x and y for inverses.
The rules
- f(g(x)) means put g(x) into f.
- Evaluate the inner function first.
- To find an inverse, swap x and y and solve for y.
- f(f⁻¹(x)) = x.
Watch out: Doing the outer function first.
Worked example
If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
- g(3) = 9.
- f(9) = 2·9 + 1 = 19.
Answer: 19
Try it yourself
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