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 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

If $${\text{f}}(8)=145$$ then $${\text{f}}(x)$$ is a function which __________ $$8$$ to $$145$$.

If $${\text{f}}(x)=5(x−11)$$ solve $${\text{f}}(x)=50$$ $$x=$${{}}.

If $${\text{f}}(x)=x^2−8x$$ solve $${\text{f}}(x)=-12$$.

If $${\text{f}}(x)=5(x−11)$$ and $${\text{g}}(x)=2x+5$$ solve $${\text{f}}(x)={\text{g}}(x)$$ $$x=$${{}}.

If $${\text{f}}(x)={7\over{3x}}$$ solve $${\text{f}}(x)=21$$.

If $${\text{f}}(x)={{5x+11}\over{2}}$$ and $${\text{g}}(x)=-{{1}\over{x}}$$ solve $${\text{f}}(x)={\text{g}}(x)$$.

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

If $${\text{f}}(x)=7x−4$$ evaluate $${\text{f}}(8)$$.

Solve $${4\over{3x+7}}={3\over{x-1}}$$ $$x=$${{}}

Starter Quiz