Question

The domain and range of the real function f defined by $f\left(x\right)=\frac{4-x}{x-4}$ is given by

• A. Domain$=R-\{-4\}$,Range $=\{-1,1\}$
• B. Domain $=R-\left\{1\right\},$ Range $R$
• C. Domain $=R,$ Range $=\{–1,1\}$
• D. Domain$=R-\left\{4\right\}$,Range $=\{-1\}$

Answer 1

The correct option is D Domain$=R-\left\{4\right\}$,Range $=\{-1\}$

Given: $f\left(x\right)=\frac{4-x}{x-4}$

$[\because \frac{f\left(x\right)}{g\left(x\right)}$ is defined when $g\left(x\right)\ne 0$ and both

f(x) and g(x) are also defined]

$\Rightarrow x-4\ne 0$

$\Rightarrow x\ne 4$

$\Rightarrow Domain=R–\left\{4\right\}$

$f\left(x\right)=\frac{4-x}{x-4}$

$f\left(x\right)=-1$

Hence, the range of$f\left(x\right)=-1$

Therefore, option (C) is correct