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Functions and Graphs (Metric)
This class covers the idea of a function, composites and inverses, odd and even functions and specific functions including the modulus function, the exponential and logarithmic functions and the hyperbolic functions. Some of this is covered at A-level, and most of the rest is Further Maths.
Functions in General
Composites, inverses, odd and even functions. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.
Functions of the form \(f(g(x))\) for given \(f\) and \(g\).
The inverse of a given function.
Odd and even functions; the odd and even parts of a function.
Modulus, Heaviside step, exponential and logarithmic functions. Apart from the Heaviside function, which is a university topic, this is covered at A-level and Science and Engineering courses will assume you know it.
The functions \(\sinh x\), \(\cosh x\) and \(\tanh x\), and their reciprocals and inverses. This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.