Question

Consider the function 𝑓⁡(𝑥) =𝑒𝑥−2 +1. What is the range of the function?

Multiple choice question.

A)
{𝑓⁡(𝑥)|𝑓⁡(𝑥) >1}


B)
{𝑓⁡(𝑥)|𝑓⁡(𝑥) <1}


C)
{𝑓⁡(𝑥)|𝑓⁡(𝑥) >2}


D)
{𝑓⁡(𝑥)|𝑓⁡(𝑥) <2}

Answer 1

A) {f(x) | f(x) > 1}

Reason: e^{x-2} > 0 for all x, so f(x) = 1 + e^{x-2} > 1. As x → -∞, e^{x-2} → 0 so values approach 1 (but never equal), and as x → ∞, e^{x-2} → ∞, so the range is (1, ∞).