The domain and range of the real function f defined by f(x) = (4-x/x-4) is given by

Question

The domain and range of the real function f defined by f(x) = (4-x/x-4) is given by (A) Domain = R, Range = -1,1  (B) Domain = R - 1 Range = R (C) Domain = R - 4 Range = - 1  (D) Domain = R - - 4 Range = -1,1

Tardigrade Admin · Accepted Answer

Given, f(x) = (4-x/x-4)=((x-4)/(x-4)) f(x) = -1 ∴ Range of f(x), x-4 ≠0 ⇒ x ≠4 ∴ x ∈ R - 4

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

Domain $= R$ , Range $= {- 1, 1}$

Domain $= R - {1}$ , Range $= R$

Domain $= R - {4}$ , Range $= {- 1}$

Domain $= R - {- 4}$ , Range $= {- 1, 1}$

Given, $f (x) = \frac{4 - x}{x - 4} = \frac{( x - 4 )}{( x - 4 )}$
$f (x) = - 1$
$∴$ Range of $f (x)$ , $x - 4 \neq = 0$
$\Rightarrow x \neq = 4$
$∴ x \in R - {4}$

Q. The domain and range of the real function f defined by f(x)=x−44−x​ is given by

Domain =R, Range ={−1,1}

Domain =R−{1}, Range =R

Domain =R−{4}, Range ={−1}

Domain =R−{−4}, Range ={−1,1}