Question

what is the range of the function y = 2e^{x}-1?
o all real numbers less than -1
o all real numbers greater than -1
o all real numbers less than 1
o all real numbers greater than 1

Explanation:

Step1: Analyze the range of \(e^{x}\)

The exponential function \(y = e^{x}\) has a range of \(e^{x}>0\) for all real \(x\).

Step2: Analyze the range of \(2e^{x}-1\)

Multiply the inequality \(e^{x}>0\) by \(2\) to get \(2e^{x}>0\). Then subtract \(1\) from each part of the inequality: \(2e^{x}-1>- 1\).

Answer:

all real numbers greater than \(-1\)