what is the range of the function ( y = 2e^{x}-1 )?\nall real numbers less than -1\nall real numbers greater…

Explanation:

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

The exponential function (e^{x}) has a range of ((0,+\infty)), i.e., (e^{x}>0).

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

Multiply the inequality (e^{x}>0) by (2). Using the property of inequalities (if (a > b) and (c>0), then (ca>cb)), we get (2e^{x}>0).

Step3: Analyze the range of (y = 2e^{x}-1)

Subtract (1) from the inequality (2e^{x}>0). Using the property of inequalities (if (a > b), then (a - c>b - c)), we have (2e^{x}-1>0 - 1). So (y> - 1).

Answer:

all real numbers greater than - 1