Question

True or False?In Exercise,determine whether the statement is true or false given that f(x) = In x.if it is false,explain why or given an example that shows it is false.

f(x - 2) = f(x) - f(2), x > 2

Answer 1

The given statement is false.

Explanation:

We are given the following in the question:

`f(x) = \text{In } x`

The given statement is

`f(x - 2) = f(x) - f(2), x > 2`

Putting the values on the right side of the given statement

`f(x-2)\\=\text{ln }(x-2) \\eq \text{ln }x - \text{ln }2`

Thus, the given statement is false.

This can be explained with the help of an example:

For x = 3

`f(x-2) = f(3-2) = f(1)\\=\text{ln }1 = 0\\f(x)-f(2)\\=\text{ln }3-\text{ln }2 \\=0.4054`