Question

find the domain and range of the real valued function f(x)=5-X/X-5

Answer 1

function is given, $f(x)=\frac{5-x}{x-5}$

domain of f(x) is the value of x in which function f(x) is defined.

for defining function, x ≠ 5
here f(x) is defined for all real number except x = 5
$domain_f\in\mathbb{R}-\{5\}$

now Range :-
f(x) = y = (5 - x)/(x - 5)

=> y = -(x - 5)/(x - 5)

=> y = -1

hence, $\text{Range}_f\in\{-1\}$