One function inside another, fg(x), and the inverse f⁻¹(x) that undoes f, including solving fg(x) = k.
What you will learn
- Work out values such as fg(2) and gf(−1)
- Find fg(x) and gf(x) as expressions
- Find f⁻¹(x) and use it
- Solve fg(x) = k
fg(x) means f(g(x))
In fg(x), g is used first, then f is applied to the result: work from the bracket outwards.
- f(x) = 2x + 1 and g(x) = x²
- fg(3) = f(g(3)) = f(9) = 19
- gf(3) = g(f(3)) = g(7) = 49
fg and gf are usually different. As expressions, fg(x) = f(x²) = 2x² + 1, and gf(x) = g(2x + 1) = (2x + 1)² = 4x² + 4x + 1.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- fg(x) means f(g(x))
- The inverse undoes the function
- Solving fg(x) = k
- Try it: See the inverse as a reflection
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
G is used first
In this unit: Functions and graph transformations
Function notation, composite and inverse functions, the shapes of standard graphs, translations and reflections of y = f(x), and the graphs of sin, cos and tan (Higher).
- Function notation
- Composite and inverse functions
- Recognising graphs
- Translating graphs
- Reflections and trigonometric graphs