Question

Let f : R⁺ → R, where R⁺ is the set of all positive real numbers, such that f(x) = log_e x. Determine

(b) {x : f(x) = −2}

Answer 1

Given:
f : R⁺ → R
and f (x) = log_ex .............(i)

(b) {x : f (x) = -2
⇒ f (x ) = -2    .....(ii)
From equations (i) and (ii), we get :
log_ex = -2
⇒ x = \[e^{- 2}\]

Hence, { x : f (x) = - 2} = { e ^{– 2}} .      [Since log_ab = c ⇒  b = a^c]