Suppose you have 2 functions: f(x) = 3x², g(x) = log₃(x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log₃(x) ( = g(x) ), then f(g(x)) = f(y) = 3y² = 3[log₃(x)]².

The part that people tend to find difficult is remembering what it means to apply a function. A simple subsitution makes this much easier. Whilst the above situation makes it seem easy, consider how much more confusing it could be if f(x) = [x⁷ + 9x⁵ + e^5x + cos(x^-1/3)]/[sin(e^x/6) + 1729*x], and g(x) was something similarly complicated; a simple substitution can do wonders and will help prevent confusion.

((x^2+4x)/2x)-((x^2-4x)/x)

Related Maths A Level answers

The curve C has parametric equations x=2cos(t) and y=3cos(2t). Find and expression for dy/dx in terms of t.

What is an easy way to remember how sin(x) and cos(x) are differentiated and integrated?

How do I evaluate composite functions?

How do I get the eigenvalues, x, of a matrix, M, with eigenvectors, v?