Suppose that the range of g lies in the domain of f so that the composition fog is defined. If f and g are one-to-one, can anything be said about fog? Give reasons for your answer.

Evaluate the integrals in Exercises 53–76.

55. ∫dx/(17+x²)

Evaluate the integrals in Exercises 91–102.

102. ∫(from -1/3 to 1/√3)(cos(arctan 3x))/(1+9x²) dx

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

12. y = ln(10/x)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

37. ∫(from x²/2 to x²)ln(√t)dt

135. Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y = e^(2x), below by the curve y = e^x, and on the right by the line x = ln(3).

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=(x+1)², x≥-1