Find the domain of the function f(x) = frac{x | vedclass

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Question

(A) The function $f(x) = \frac{x^{2}+3x+5}{x^{2}-5x+4}$ is defined for all real values of $x$ except where the denominator is zero.Set the denominator

Vedclass · Accepted Answer

$R - \{1, 4\}$

Vedclass · Answer

(A) The function $f(x) = \frac{x^{2}+3x+5}{x^{2}-5x+4}$ is defined for all real values of $x$ except where the denominator is zero.Set the denominator equal to zero: $x^{2}-5x+4 = 0$.Factor the quadratic expression: $(x-4)(x-1) = 0$.This gives $x = 4$ or $x = 1$.Therefore,the function is undefined at $x = 1$ and $x = 4$.The domain of the function is the set of all real numbers except $1$ and $4$,which is written as $R - \{1, 4\}$.

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

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