Question

Find the domain and the range of f(x)=2-x+sin x

Answer 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.(−∞,∞)-∞,∞{x|x∈R}x|x∈ℝFind the magnitude of the trig term sin(x)sinx by taking the absolute value of the coefficient.11The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.y=−1y=-1The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.y=1y=1The range is −1≤y≤1-1≤y≤1.[−1,1]-1,1{y|−1≤y≤1}y|-1≤y≤1Determine the domain and range.Domain: (−∞,∞),{x|x∈R}-∞,∞,x|x∈ℝRange: [−1,1],{y|−1≤y≤1}