# Find the domain of the real valued rational function f given below. f(x) = \frac{(x - 1) }{ (x - 3)}

## Question:

Find the domain of the real valued rational function {eq}f {/eq} given below.

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

## Domain of Rational Function:

Domain of a function {eq}f(x) {/eq} means where it is defined.

Now:

If {eq}f(x) {/eq} is a rational function then the function will be defined at all real values of {eq}x {/eq} except where the denominator is zero.

Suppose {eq}f(x) = \frac{p(x)}{q(x)} {/eq} then for finding the domain of this rational function we have to set {eq}q(x) = 0 {/eq}

From the equation {eq}q(x) = 0 {/eq} , we will get {eq}x {/eq} values. The domain {eq}f(x) {/eq} will be all real values except these {eq}x {/eq} values.

In the rational function, {eq}p(x) \, and \, q(x) {/eq} are polynomial functions and {eq}q(x) \neq 0 {/eq}

The rational function is given by:

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

For finding the domain of this function, we have to set {eq}x - 3 = 0 {/eq}

Hence:

{eq}x - 3 = 0 \\ \Rightarrow x = 3 {/eq}

So:

The domain of the function is the set of all real values except {eq}3 {/eq}