Investigate the inverse of a composite function. In parts b and c, which involve graphing be sure the same size unit and scale on both axes so that symmetry about the line y = x can be checked visually.
a) Let f(x) = 2x+1 and g(x) = 1/4 x -3. Compute each of the folowing:
(i) f(g(x)) (ii) g(f(x)) (iii) f^-1 (x) (iv) g^-1(x) (v) f^-1(g^-1(x)) (vi) g^-1(f^-1(x))
b) on the same set of axes, graph the two answers that you obtained in (i) and (v) of part a. Note that the graphs are not symetric about y =x. the conclusion here is that the inverse function for f(g(x)) is not f^-1(g^-1(x)).
c) On the same set of axes, graph the two answers that you obtained in (i) and (vi) of part a, also put the line y = x into the picture. Note that the two graphs are symetric about the line y=x.The conclusion is that the inverse function for f(g(x)) is g^-1(f^-1(x)).