Find the Domain 4.5=e^(1-0.5x)+e^(0.5x-1)

Problem

4.5=e^(1−0.5*x)+e^(0.5*x−1)

Solution

1. Identify the type of equation and the functions involved. The equation consists of exponential functions of the form e^ƒ(x)

2. Determine the domain of the individual components. The exponential function e^u is defined for all real numbers u

3. Analyze the exponents $1 - 0.5xa*n*d.5x - 1.B*o*t*h*a*r*e*l*i*n*e*a*r*p*o*l*y*n*o*m*i*a*l*s,w*h*i*c*h*a*r*e*d(e)*ƒ*i*n*e*d(ƒ)*o*r*a*l*l*r*e*a*l*v*a*l*u*e*s(o)*ƒ$.

4. Conclude that since there are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers, there are no restrictions on x

Final Answer

Domain=(−∞,∞)

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