Question

Find the domain of the function:
$f\left(x\right)=\frac{x^2+3x+5}{x^2-5x+4}$

• A. R – {1, -4}
• B. R – {-1, 4}
• C. R – {-1, -4}
• D. R – {1, 4}

Answer 1

The correct option is D R – {1, 4}

Domain of a real-valued function is the set of values where function is defined.
$\text{Given,}f\left(x\right)=\frac{x^2+3x+5}{x^2-5x+4}$
The function can be defined when denominator $\ne$ 0
$\Rightarrow x^2-5x+4\ne 0$
$\Rightarrow (x-4)(x-1)\ne 0$
$\Rightarrow x\ne 4\text{and}1$
$\therefore$ The function is defined for all real numbers except at x = 4 and x = 1.
Hence, domain of the function is R – {1, 4}.