A Level Maths Session

Inverse Function

Exponential Function

Maclaurin Series

Complex Number Exponential Form

Inverse Function

Hi Everyone,

Welcome to this session.

proof inverse function existence

Exercises

Please try these questions.

1. Consider the functions f(x) = x²+5 and g(x) = 2x. When x = 2, calculate the values of f(x), g(x), fg(x) and f^-1(x).

2. Consider the mapping x → x²+5. Given that the domain is 0 < x < 1 and that the codomain is 4 < y < 6. Sketch a graph of y = x²+5. Why is this a function?

3. Consider the inverse mapping. Why is this not a function? If we can change the codomain, what can we do make this inverse mapping a function?

4. Let f(x) = x² + 5. Write this using the f and → notation. Using the new codomain of f, find the inverse function f^-1. State the domain and codomain of f^-1.

5. g(x) = 2x has domain 0 < x < 1 and codomain 0 < y < 2. Sketch a graph of y = g(x). Why is f(g(x)) not a function?

Past Exam Questions

In this video, I shall go through some past exam questions.

2007 H2 maths P1 Q2

Thanks for attending this session.

Dr Hock
9 May 2014