A function is a mathematical relationship that uniquely maps values of one set to the values of another set.

An equation is used to show two expressions that are equal to each other.

Solving equations involving 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

For the function $${\text{fg}}(x)$$ the $$x$$ values are in the domain and the values of $${\text{fg}}(x)$$ are in the __________.

If $${\text{f}}(x)=3x$$ and $${\text{g}}(x)=2x+9$$ solve $${\text{fg}}(x)=-3$$ $$x=$${{}}.

If $${\text{f}}(x)=3x$$ and $${\text{g}}(x)=2x+9$$ solve $${\text{gf}}(x)=-3$$ $$x=$${{}}.

If $${\text{f}}(x)=3x$$ and $${\text{g}}(x)=2x+9$$ solve $${\text{fg}}(x)={\text{gf}}(x)$$.

When we input our solution into function the input and output are equal.

If $${\text{f}}(x)=2x-7$$ what do you notice when we solve $${\text{f}}(x)={\text{f}}^{-1}(x)$$?

If $${\text{f}}(x)=7-2x$$ and $${\text{g}}(x)=x^2$$ solve $${\text{gf}}(x)=9$$.

$${\text{fg}}(x)$$, $${\text{fgh}}(x)$$, and $${\text{fff}}(x)$$ are all examples of __________.

If $${\text{f}}(x)=7x−4$$ and $${\text{g}}(x)=3x$$ evaluate $${\text{gf}}(11)$$.

If $${\text{f}}(x)=6x−15$$ solve $${\text{f}}(x)=57$$ $$x=$${{}}.

If $${\text{f}}(x)=7x−4$$ and $${\text{g}}(x)=3x$$ which is an expression for $${\text{gf}}(x)$$?

Starter Quiz