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Q.
The domain and range of the real function $f$ defined by $f\left(x\right) = \frac{4-x}{x-4}$ is given by
Relations and Functions
Solution:
Given, $f\left(x\right) = \frac{4-x}{x-4}=\frac{\left(x-4\right)}{\left(x-4\right)}$
$f\left(x\right) = -1$
$\therefore $ Range of $f\left(x\right)$, $x-4 \ne0$
$\Rightarrow x \ne4$
$\therefore x \in R - \left\{4\right\}$