## 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.- 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). - 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?
- 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?
- 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}. - 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.

Thanks for attending this session.

Dr Hock

9 May 2014