Algebraic fractions can be cancelled down. The numerators and denominators must be fully factorised first.

If numerator and denominaros contain fractions then you can multiply both by the lowest common multiple to create an equivalent fraction

to multiply fractions, multiply the numerators and multiply the denominators

To divide two fractions, multiply the first fraction by the reciprocal of the second.

To add (or subtract) fractions, each one must have the same denominator. Find lowest common multiple to do this.

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Functions

A one-to-one function is wwhere every element of the domain is mapped tto one element in the range.

Many mappings can be made into functions by changing the domain. E.g. the mapping 'positive square root' can be changed into the function f(x)=√x by having a domain of x>0

A composite function is two or more functions combined:

g(x)=2x + 3, f(x)= x^{2}

fg(4)=f(2 x 4 + 3) = f(11) = 121

The inverse funtion performs the opposite operation to the function. To calculate the inverse, change the subject of the formula.

The range of the function is the domain of the inverse. The domain of the function is the range of the inverse.

The inverse graph is a reflection of the function in the line y = x

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