1.Show that the function f(x) = ln(x² + 1) is one-to-one for x > 0. Graphing does not count as proof. (Hint: Use the derivative of the function.)

2.Find a formula for the inverse function f^{- 1}(x) of f(x) = 2x/x+1.

Verify that f(f^{- 1}(3)) = 3 and (f^{- 1}f(5) = 5.

3.Fill in the values of f^{- 1}(x) and (f^{- 1} )' (x) for x = 0, 1, 2. Provide detail to support your answers.

x f(x) f'(x) f^-1(x) ( f^-1)'(x)

0 1 4

1 2 -2

2 0 1

4.Determine the lengths of the sides of a right triangle so one angle is = arccos(4/5). Use a triangle to determine the values of sin and tan

5.Calculate the derivatives.

(a) y = (arccos(x) + 1)⁵

(b) y = arcsin (x² + x)

(c) y = ln(arc csc x)

6.Evaluate each integral based on inverse trigonometric functions. An answer with insufficient detail will not receive full credit.

(a) dx/1-4x²

(b) (e^t/ e^2t + 4) dt

(c) (1/ x 25x² - 49)dx