Find the range 

f(x)= root 9-x^2

my doubt is that the answer says [0,3]. But since we have a square root, won't we get range [-3,3]?

Asked by fishtailfever | 15th Feb, 2020, 05:11: PM

Expert Answer:

To find the range of the given function:
f left parenthesis x right parenthesis equals square root of 9 minus x squared end root
D o m a i n space o f space f left parenthesis x right parenthesis space i s space left square bracket negative 3 comma space 3 right square bracket
N o w comma space 9 minus x squared greater or equal than 0 space a l w a y s
therefore space M i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis space i s space 0
square root of 9 minus x squared end root space t a k e s space t h e space m a x i m u m space v a l u e space a t space t h e space m i d p o i n t space o f space t h e space i n t e r v a l space left square bracket negative 3 comma space 3 right square bracket
therefore space M a x i m u m space v a l u e space o f space square root of 9 minus 0 squared end root equals 3
H e n c e comma space R a n g e space o f space f left parenthesis x right parenthesis space i s space left square bracket 0 comma space 3 right square bracket

Answered by Renu Varma | 17th Feb, 2020, 11:03: AM