State the domain and range of the function

f(x) = 2sin(sqrt(3x-1)) + 3

Why is this so difficult?

2 answers

no idea. Just take it step by step.

domain of √x is x>=0
so, the domain of √(3x-1) is 3x-1 >= 0, or x >= 1/3

the domain of sin(x) is all reals, so

the domain of sin(√(3x-1)) is the domain of √(3x-1), or x >= 1/3
of course, the range is just the same as the range of 2sin(x)+3: [1,5]

http://www.wolframalpha.com/input/?i=2sin(sqrt(3x-1))+%2B+3