Find domain and range

Question

Answer 1

Domain and range of f(x) = 1/(6 + e^x)

Domain

Since e^x > 0 for all x this means 6 + e^x > 0 for all x

Since the denominator is never zero, the domain includes all values of x

So the domain of f(x) is (–∞,∞)

Range

As x → –∞ e^x → 0 and f(x) → 1/6 (horizontal asymptote = 1/6 at –∞)

As x → ∞ e^x → ∞ and f(x) → 0 (horizontal asymptote = 0 at ∞)

0 < f(x) < 1/6 for all values of x

So the range of f(x) is (0,1/6)