Question Type 3: Finding domain and range of logarithmic and exponential functions Exercises

Determine the range of $f(x) = x^2 e^x$.

Find the domain of $f(x) = \ln(4x + 5)$.

Determine the range of $h(x) = x e^{x+4}$.

Find the domain of $h(x) = \ln(x^2 - 4)$.

Find the domain of $f(x) = \ln(x^2 - 2x - 3)$.

Determine the range of $f(x) = 3e^{-x}$.

Find the domain of $f(x) = \ln\left(\frac{x-1}{x+2}\right)$.

Find the range of $f(x) = e^{2x}$.

Determine the domain of $f(x) = \ln(5 - x^2)$.

Determine the range of $f(x) = \frac{e^x}{1 + e^x}$.

Find the range of $f(x) = e^x + e^{-x}$.

Determine the domain of $g(x) = \log_{2}(3 - x)$.