Question

Find the domain of $\bf f(x) = \cfrac{x²+3x+5}{x²-5x+4}$

Option :-

$\bf \quad 1. \quad \mathbb R \bf - \{4\}$

$\bf \quad 2. \quad \mathbb R \bf - \{0\}$

$\bf \quad 3. \quad \mathbb R \bf - \{1,4\}$

$\bf \quad 1. \quad \mathbb R \bf - \{1\}$​

Answer 1

Answer:

R-[1,4]

is your answer.

Answer 2

Step-by-step explanation:

We have,

$f(x) = \dfrac{ {x}^{2} + 3x + 5 }{ {x}^{2} - 5x + 4 }$

$\implies \: f(x) = \dfrac{ {x}^{2} + 3x + 5 }{ {x}^{2} - 4x - x + 4 }$

$\implies \: f(x) = \dfrac{ {x}^{2} + 3x + 5 }{ x(x - 4) - 1(x - 4 )}$

$\implies \: f(x) = \dfrac{ {x}^{2} + 3x + 5 }{( x - 1)(x - 4) }$

To be defined,

$\implies \:( x - 1)(x - 4) \ne0$

$\implies \: x \ne 1 \: \: \: or \: \: \: x \ne4$

$\therefore dom \big( f(x)\big) \in \: R - \{1,4 \}$