01/09/2025
Language of Functions (Cambridge (CIE) IGCSE Additional Maths)
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Introduction to functions:
What is a mapping?
A mapping takes an 'input' from one set of values to an 'output' in another
What notation is used for functions?
Functions are denoted by straight f open parentheses x close parentheses comma space straight g open parentheses x close parentheses, etc
e.g. straight f open parentheses x close parentheses equals x squared minus 3 x plus 2
These would be pronounced as 'f of x', 'g of x', etc
There is an alternative notation
e.g. straight f colon x rightwards arrow from bar x squared minus 3 x plus 2
Which may be pronounced 'the function f maps x to x-squared minus three x plus two'
How does a function work?
A function has an input open parentheses x close parentheses and output left parenthesis straight f open parentheses x close parentheses space or space space y right parenthesis
Whatever goes in the bracket (instead of x) with f, replaces the x on the other side
This is the input
If the input is known, the output can be calculated
For example, given the function straight f left parenthesis x right parenthesis space equals space 2 x space plus space 1
straight f left parenthesis 3 right parenthesis space equals space 2 space cross times space 3 space plus space 1 equals 7
straight f left parenthesis negative 4 right parenthesis space equals space 2 space cross times space left parenthesis negative 4 right parenthesis space plus space 1 space equals space minus 7
straight f left parenthesis a right parenthesis space equals space 2 a space plus space 1
If the output is known, an equation can be formed and solved to find the input
For example, given the function straight f left parenthesis x right parenthesis space equals space 2 x space plus space 1
If straight f left parenthesis x right parenthesis space equals space 15, the equation 2 x space plus space 1 space equals space 15 can be formed
Solving this equation gives an input of 7
Worked Example
A function is defined as straight f open parentheses x close parentheses space equals space 3 x to the power of 2 space end exponent minus space 2 x space plus space 1.
a) Find straight f open parentheses 7 close parentheses.
