Exercise 4: (a) Let f: X → R, with X C R, be an injective function. Show that the graph of f is given by the graph of f, reflected over the line y = x. (b) Use this principal to graph the inverse of f : (-1/2,7/2) –→ R, with f(x) = tan(x). Remark: This is a very common method for graphing inverse functions, especially since they fre- quently do not have a nice form.

Q: The graph of g: ,0→R, g(x)=(x+1)(x¹+x²-x+1) is shown below. -2 2 1 -2 y +x 2 f. Sketch the graph of…

A:

Q: Let f (x) = Vx and g(x) = - Find the formulas for all four compositions x2 f(f(x)), g(g(x),…

A:

Q: Find the inverse function of f.

A: An inverse function is reverse of the given function. In simple words if a function f takes input…

Q: Let f(x) = (x−³+4)5 – 1.

A: Assume that y=f(x) and use the description of f(x) and then express x in terms of y, that formula in…

Q: Give an example of a one-to-one function f(x) that is its own inverse f-1(x) so that f(x)=f-1(x).

A:

Q: The function f(x): х is one-to-one. (a) Find the inverse of f and check the answer. (b) Find the…

A:

Q: Find the inverse function of f. f(x) = 4 - x2, x ≥ 0

A: Given f(x) = 4 - x2, x ≥ 0

Q: e) Let f(x) be the graph shown. Draw the inverse of f(x)

A:

Q: The function f is defined by f(x) = -x³ + x² - 4x and the point (1, -4) is on the graph of f. If g…

A:

Q: Find a method that uses the Dot-Product to decide for three randomly chosen points P, Q, and R in…

A: Let us sketch a figure relating to the problem