Question

a.)Consider the function f (x) = 3x/ x^2 +1

i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the same for f (2x) and 2f (x).

ii) Sketch y = f (x) on the interval [−2, 2].

iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each case, if a solution does not exist, explain.

iv) What is the domain of f (x)?

b.)Let f (x) = √x −1 and g (x) = x 2 −3.

i) Find f ◦ g (x) and g ◦ f (x), and then compare their domains.

ii) Find a function h(x) such that h ◦ f (x) = x for all x in the domain of f (x)

c.) Let f (x) = x^2 + x +3. Find the difference quotient and simplify

Answer 1