Question

f(x) =1÷4x-3 then find domain of f​

Answer 1

$R - \{{3/4 \}}$

Step-by-step explanation:

$given \: \: \: \: f(x) = \frac{1}{4x - 3} \\ f(x) \: \: is \: \: defined \: \: if \: \: 4x - 3≠ 0 \\then \: \: \: x ≠ \frac{3}{4} \\ so \: \: \: \: domain \: \: of \: \: f(x) \: \: is \: \: R - \{{3/4 \}}$

Answer 2

Given :-

$\quad \leadsto \quad \sf f ( x ) = \dfrac{1}{4x - 3}$

To Find :-

Domain of $\sf f ( x )$

Solution :-

At first let's see the function carefully ;

$\quad \leadsto \quad \bf f ( x ) = \dfrac{1}{4x - 3}$

Here , The denominator i.e $\sf 4x - 3$ shouldn't equal to 0 , to be defined!

Because , as the Denominator became 0 then we obtain $\sf f ( x ) = \dfrac{1}{0} = \infty$ , that is not defined . So ;

$\quad \leadsto \quad \sf 4x - 3 \neq 0$

${ : \implies \quad \sf 4x \neq 3 }$

${ : \implies \quad \sf x \neq \dfrac{3}{4}}$

So , Here , 'x' Is defined for all values of $\sf x \in \mathbb R$ , except $\dfrac{3}{4}$ . So , let's use difference of set for the domain of $\sf f(x)$

After using difference of set . Domain $\blue \{$ $\sf f ( x )$ $\blue \}$ is

• $\mathbb R - \sf \bigg\{ \dfrac{3}{4} \bigg\}$

$\quad \qquad { \bigstar { \underline { \boxed { \pmb { \bf { \red { \underbrace { \therefore Domain \: of \: f ( x ) = \mathbb R \bf - \bigg\{ \dfrac{3}{4} \bigg\}}}}}}}}}{\bigstar}\quad \qquad$