finding range of f(x)= √(1-e^x+2)

Question

i was able to find the domain of f(x)= √(1-e^x+2)

i set 1-e^x+2 >/= 0 

and i found that x</= -2

 

How would i determine the range? 

Answer 1

I think that you need to parenthesize the exponent (x+2).

The minimum value of e^x+2 is > 0 but negligbly small so the maximum value of f(x) is essentially 1.

Range: [0,1)