Find the Domain f(x)=sin(e^(-x))

Problem

ƒ(x)=sin(e(−x))

Solution

1. Identify the outer function, which is the sine function sin(u) The domain of sin(u) is all real numbers, (−∞,∞)

2. Identify the inner function, which is the exponential function e(−x) The domain of ev is all real numbers, (−∞,∞)

3. Analyze the exponent −x The expression −x is a polynomial (linear) function, which is defined for all real numbers.

4. Determine the composition constraints. Since there are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers, the function is defined for all real values of x

Final Answer

Domain: *(−∞,∞)

Want more problems? Check here!