Soumya Biswas

(iii) f(x) = x, x is a real number

1. Min as you put larger values of x the function goes on decreasing thus for very large value of X   f goes on decreasing 

Thus min is - inf 

Max when x is min which is just lesser than 2 as x greater 0 

Thus range is open - inf to open 2

(i) f(x) = –|x| (ii)

Domain is the real values which are allowed to compose the given function 

F = - mod (x) allows all real values of X as domain but in the range all the negative values. 0 to - inf   as mod x gives positive values - of mod x gives all negative 

2. For t to be real 9- squ (x) must be greater 0 

9 - squ (x) greater 0 

Squ ( x) less than 9 

Factorize x- 3 ×  x+ 3 less 0     x between -3 to 3 . Range is from min to max 

Min is 0 when x=3       Max is 3 when x= 0

Thus from 0 to 3 both including.

When 1 value of y gets mapped from 2 values of X makes f a non function 

Let easy be the way when a+ b = 0 , a = -b 

ab = - a×a  which is multiple 

E.g. - 4 = -2× 2     -2 + 2 = 0

         -9 = -3×3     -3 + 3 = 0 

Hence this is many to one which is not a function