Question

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

Answer 1

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
$\Rightarrow x^2-5x+4\ne 0$
$\Rightarrow (x-4)(x-1)\ne 0$
$\Rightarrow x\ne 4\text{and}1$ [1 mark]
$\therefore$ The function is defined for all real numbers except at x = 4 and x = 1.
Hence, domain of the function is R – {1, 4}. [1 mark]