## Function Notation

### Linear Equations

It is possible to prove that for f(x):

However we can see that this not true for g(x), which is a linear equation with a small shift:

### Inverse Equations

An inverse equation has different properties to a linear equation

Since,

The left hand side needs to be multiplied by (x+y) in order to equal the right hand side therefore:

### Exponential and Logarithmic Functions

Logarithmic functions have the characteristic that adding two logs together is the same as multiplication of the variables:

Exponential functions have the characteristic that multiplying to exponentials together is the same as addition for the variables:

### Example

**2013 exam 2**

In order to answer this question we need to substitute the notation from the questions and see which works

Only C works and that is our answer

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