1. Show that the function f (x) = exs+2x+1 is one-to-one. Graphing does not count as proof. (Hint: Use the derivative of the function.) 2. Find a formula for the inverse function f (x) off (x) = 3 - In (x). Verify that f-1(f(e?)) = e7 3. Fill in the values of f-1(x) and (f-1)'(x) for x = -1, 1, 2. Provide detail to support your answers. x f(x) f' (x ) f-1(x) (f-1)'(x) - 1 -1 0 1 2 -2 2 1 4 4. In the triangle below, angle 0 is (a) the arcsine of what number? (b) the arctangent of what number? (c) the arcsecant of what number? (d) the arccosine of what number? 3 45. Calculate the derivatives. (a) y = (arctan(x) +5) (b) y = tan(x2 + 1) . arcsin(x) (c) y = In[arcsec(x)] 6. Evaluate each integral based on inverse trigonometric functions. An answer with no sufficient detail will not receive full credits. (a) - dx V1-16x2 ( b) [ - 1 =dx xV16x2 -25 e2t (c) p4t -dt