The domain of the function f: R rightarrow R | vedclass

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Question

(C) For the function $f(x) = \sqrt{x^{2}-7x+12}$ to be defined,the expression inside the square root must be non-negative: $x^{2}-7x+12 \geq 0$ Factor

Vedclass · Accepted Answer

$(-\infty, 3] \cup [4, \infty)$

Vedclass · Answer

(C) For the function $f(x) = \sqrt{x^{2}-7x+12}$ to be defined,the expression inside the square root must be non-negative: $x^{2}-7x+12 \geq 0$ Factorizing the quadratic expression: $(x-4)(x-3) \geq 0$ Using the sign scheme method for the inequality,the expression is non-negative when $x \leq 3$ or $x \geq 4$. Thus,the domain is $x \in (-\infty, 3] \cup [4, \infty)$.

The domain of the function $f: R \rightarrow R$ defined by $f(x) = \sqrt{x^{2}-7x+12}$ is

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