1.

Find the domain of the real valued function f(x)=1/log(2-x)​

Answer»

ave to find domain of the given function :-

\rm \large f(x) = \dfrac{1}{log (<klux>2</klux>-x)}

We KNOW that DENOMINATOR cannot be zero.

\rm \longrightarrow log (2-x) \ne0 \\ \\ \rm \longrightarrow (2-x) \ne {e}^{0} \\ \\ \rm \longrightarrow 2-x \ne 1\\ \\ \rm \longrightarrow 2 - 1 \ne x\\ \\ \rm \longrightarrow 1 \ne x\\ \\ \rm \longrightarrow x \ne 1 \: \: \: \: ...(1)

Also,

\large \rm \longrightarrow 2 - x > 0 \\ \\ \large \rm \longrightarrow 2 > x \: \: ...(2)

From EQUATION (1) and (2) :-

\rm D_f = x \in (- \infty, 2) - \{1 \} \\ or \\ \rm D_f = x \in (- \infty, 1) \cup (1,2) \\ \\ \rm \: where \: D_f \: is \: domain \: of \: the \: function


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