The composite function gf($$x$$) is the combination of f($$x$$) and g($$x$$). The output from f($$x$$) is the input for g($$x$$).

Writing composite functions

Maths

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

Functions and proof

__________ function is where another function is applied to the output of a function.

The output of $${\text{g}}(8)$$ being input in to $${\text{f}}(x)$$

The output of $${\text{f}}(8)$$ being input in to $${\text{g}}(x)$$

The output of $${\text{g}}(8)$$ being input in to $${\text{h}}(x)$$

The output of $${\text{h}}(8)$$ being input in to $${\text{g}}(x)$$

The output of $${\text{f}}(8)$$ being input in to $${\text{f}}(x)$$

Match the notation to the correct language.

If $${\text{f}}(x)=2x$$ and $${\text{g}}(x)=5x-1$$ then $${\text{fg}}(5)=$${{}}.

If $${\text{f}}(x)=2x$$ and $${\text{g}}(x)=5x-1$$ then $${\text{gf}}(5)=$${{}}.

If $${\text{f}}(x)=9x$$ and $${\text{g}}(x)=3-2x$$ how do we express the function $${\text{fg}}(x)$$?

If $${\text{f}}(x)=x^2$$ and $${\text{g}}(x)=3-2x$$, how do we express the function $${\text{fg}}(x)$$?

For the function $$\text{f}(x)$$ if $$\text{f}(10)=35$$ then $$10$$ is a value in the...

If $$\text{f}(x)=5x$$, $$\text{g}(x)=3x+4$$ and $$\text{h}(x)=1-2x$$ evaluate and order the below from greatest to smallest value.

This lesson will be removed by end of Summer Term 2025.

Writing composite functions

Lesson outcome

This lesson will be removed by end of Summer Term 2025.