MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
Consider the exponential function y=(21)x.
(i) Obtain the inverse of this function in logarithmic form.
(ii) Sketch, on the same set of axes, the graphs of y=(21)x and its inverse obtained in part (i). Clearly indicate the intercepts with the axes, the vertical asymptote, and the line of symmetry.
(iii) Using analytical reasoning, verify that each point (p,q) on y=(21)x corresponds to the point (q,p) on its inverse. Hence justify why the two curves are mirror images about the line y=x. State any assumptions made.