Let f: R+→ R, where R+ is the set of all positive real numbers, be such that f(x) = loge x. Determine (i) the image set of the domain of f (ii) {x: f (x) = –2}

Answers:

(i)

Domain of f = R⁺

Value of logarithm to the base e (natural logarithm) can take all possible real values.

∴ The image set of f = R

(ii)

f(x) = –2

log_e x = –2

∴ x = e^-2 [log_b a = c ⇒ a = b^c]

∴ {x: f(x) = –2} = {e^–2}