Inverse functions:
1i) Let f(x)=ln(x+3) sketch the mirror line of y=x on the axes. Sketch f(x) on the axes.
ii) Indicate the domain and range of f(x).
iii) Is f(x) a one-to-one function? Explain this algebraically and graphically by using appropriate tests.
iv) Find the inverse function of f(x).Show all steps and sketch and label the inverse function on the previousgraph of question 1i.
v) Indicate the domain and range of the inverse function.Compare the domain and range of f(x) and of the inverse f(x);what statement can be made about them.
vi)Let g be the inverse function in part iv. Show that g o f(x)=x and g o f(y)=y (show all your steps.)
2)Use trigonometric identities to establish the following identity:
Show that cos(x+pi/2)=-sin(x)
3a) Evaluate lim(x-->infinity) ln(x^50)/x^100. Please reference any theorems and examples that you used to answer this question.
b)A hiker leaves his cabin at 7:00am and takes his usual path to the top of the mountain, arriving at 7:00pm.The following morning he starts at 7:00am at the top and takes the same path back ,arriving at his cabin at 7:00pm.USE THE INTERMEDIATE VALUE THEOREM to explain that their is point on the path that the hiker will cross exactly at the same time of day at both days.