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If $\mathrm{f}(\mathrm{x})=\frac{\sqrt{\mathrm{x}-1}}{\mathrm{x}-4}$ defines a function of $\mathrm{R}$, then what is its domain?
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Verified Answer
The correct answer is:
$[1,4) \cup(4, \infty)$
$f(x)=\frac{\sqrt{x-1}}{x-4}$
$f(x)$ is defined for $(x-1) \geq 0 \Rightarrow x \geq 1$ and $x-4 \neq 0$ $\Rightarrow x \neq 4$
$\therefore \quad$ Domain of $f(x)=1 \leq x < \infty-\{4\}$
or, $\quad x=[1,4) \cup(4, \infty)$.
$f(x)$ is defined for $(x-1) \geq 0 \Rightarrow x \geq 1$ and $x-4 \neq 0$ $\Rightarrow x \neq 4$
$\therefore \quad$ Domain of $f(x)=1 \leq x < \infty-\{4\}$
or, $\quad x=[1,4) \cup(4, \infty)$.
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