Writing composite functions
I can write a composite function both numerically and algebraically.
- Year 11
Writing composite functions
I can write a composite function both numerically and algebraically.
Lesson details
Key learning points
- Using function notation, you can write a composite function.
- Function notation can be replaced with the algebraic form.
- An input can be substituted in and the numerical output found.
Keywords
Composite function - The composite function gf($$x$$) is the combination of f($$x$$) and g($$x$$). The output from f($$x$$) is the input for g($$x$$).
Common misconception
Pupils may try to evaluate composite functions by working from left to right.
Remind pupils that they cannot do this as each function needs an input and with composite functions the input needs to be evaluated before it can be used.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.For the function $$\text{f}(x)$$ if $$\text{f}(10)=35$$ then $$10$$ is a value in the...
Q2.Simplify $$3x + 12 - x - 7$$.
Q3.Simplify $$4(x-3)+x-3$$.
Q4.Expand and simplify $$(x+5)^2+(x+5)$$.
Q5.Expand and simplify $$2(x+5)-(x+8)$$.
Q6.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.
Assessment exit quiz
6 Questions
Q1.__________ function is where another function is applied to the output of a function.
Q2.Match the notation to the correct language.
$${\text{fg}}(8)$$ -Â The output of $${\text{g}}(8)$$ being input in to $${\text{f}}(x)$$
$${\text{gf}}(8)$$ -Â The output of $${\text{f}}(8)$$ being input in to $${\text{g}}(x)$$
$${\text{hg}}(8)$$ -Â The output of $${\text{g}}(8)$$ being input in to $${\text{h}}(x)$$
$${\text{gh}}(8)$$ -Â The output of $${\text{h}}(8)$$ being input in to $${\text{g}}(x)$$
$${\text{ff}}(8)$$ -Â The output of $${\text{f}}(8)$$ being input in to $${\text{f}}(x)$$
Q3.If $${\text{f}}(x)=2x$$ and $${\text{g}}(x)=5x-1$$ then $${\text{fg}}(5)=$$ .
Q4.If $${\text{f}}(x)=2x$$ and $${\text{g}}(x)=5x-1$$ then $${\text{gf}}(5)=$$ .
Q5.If $${\text{f}}(x)=9x$$ and $${\text{g}}(x)=3-2x$$ how do we express the function $${\text{fg}}(x)$$?
Q6.If $${\text{f}}(x)=x^2$$ and $${\text{g}}(x)=3-2x$$, how do we express the function $${\text{fg}}(x)$$?
