Mathematics

Problem

The function

f:\mathbb R\to\mathbb R

is defined by

f(x)=3-x

for all real

x

. Attempt all parts. a. (i) State the definition of the inverse of a bijective function. b. (ii) The points

A(2,1)

B(-1,4)

and

C(5,-2)

lie on the graph of

f

. Write the coordinates of their corresponding images

A'

B'

and

C'

on the graph of

f^{-1}

. c. (iii) On the same pair of axes, sketch the graphs of

f

and

f^{-1}

. Clearly mark the points

A, B, C

and their images. d. (iv) From your sketch, describe (in not more than two sentences) the relation between the two graphs and the line

y=x

. e. (v) Write the domain and the range of

f

and of

f^{-1}