Question

If the composition of two functions is:

Answer 1

Answer:

R-{3}

Step-by-step explanation:

Given is a function

$f(x) = \frac{1}{x-3}$

The domain is the possible values which x can take

Here on analysing the function we find that f(x) becomes undefined when denominator =0

i.e. $x-3 \neq 0\\x\neq 3$

There cannot be any other restriction as there is no square root sign.

Hence domain is set of all real numbers except 3

In interval notation domain = $(-\infty, 3)U(3,\infty)$

Answer 2

You are correct! The problems that can arise with a function domain are:

• Denominators that become zero
• Even-degree roots with negative input
• Logarithms with negative or zero input

In this case, you have a denominator, and you don't have roots nor logarithms. This means that your only concern must be the denominator, specifically, it cannot be zero.

And you simply have

$x-3\neq 0 \iff x \neq 3$

So, the domain of this function includes every number except 3.