A2 Pure Maths - Algebra and Functions

Key Knowledge Points

Modulus Graphs

Where f(x) is positive, so is the modulus, but where f(x) is negative, the modulus is a reflection

f^-1(x)

only exists where f(x) is a one to one function

graph of f^-1(x)

a reflection of f(x) in the line y=x

domains and ranges of inverse functions

swap i.e. domain of f(x) becomes range of f^-1(x)

domain of fg(x)

equivalent to domain of g(x)

graph transformations - inside

affects x coordinate and does the opposite

graph transformations - outside

affects y coordinate and does the same