How do I evaluate composite functions?

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 + e5x + cos(x-1/3)]/[sin(ex/6) + 1729*x], and g(x) was something similarly complicated; a simple substitution can do wonders and will help prevent confusion.

SG
Answered by Seb G. Maths tutor

4084 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the differential of y =sin(2x)?


(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).


Find d/dx (ln(2x^3+x+8))


Express (3-5x)/(x+3)^2 in the form A/(x+3) + B/(x+3)^2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences