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Question
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(b) {x : f(x) = −2}
Solution
Given:
f : R+ → R
and f (x) = logex .............(i)
(b) {x : f (x) = -2
⇒ f (x ) = -2 .....(ii)
From equations (i) and (ii), we get :
logex = -2
⇒ x = \[e^{- 2}\]
Hence, { x : f (x) = - 2} = { e – 2} . [Since logab = c ⇒ b = ac]
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