Mathematics

Problem

Consider the function

p: \mathbb R \to \mathbb R

defined by

p(x)=x^{2}-4x+3

. (i) Find the images of

-1

and

5

under

p

. (ii) Solve the equation

p(x)=0

and interpret your answers as pre-images of the output

0

. (iii) For how many real numbers

y

does the equation

p(x)=y

have exactly one real solution for

x

? Give the set of all such

y

and justify your answer fully. a. a.