Math, asked by llismeTeraGhatall, 2 months ago

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

Answers

Answered by Ranveerx107
2
  • We have to find domain of the given function :-

 \rm  \large f(x) =  \dfrac{1}{log (2-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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