Question

Find the domain of the real valued function: f(x) = $\frac{1}{log(2 - x)}$

Answer 1

The $\textbf{domain}$ of function $\textbf{f(x)}$ is the set of all values for which function is defined.

we have to find domain of function : f(x) = $\frac{1}{log(2-x)}$

To define f(x),
denominator of f(x) ≠ 0
and (2 - x) > 0 [ for log to be defined ]

e.g., log(2 - x) ≠ 0

or, 2 - x ≠ 1

or, x ≠ 1

and (2 - x) > 0 or, 2 > x


hence, domain of function f(x) $\in (-\infty,2)-\{1\}$