What is the domain and range of # F(X)=1-x^2#?

1 Answer
Alan P.
Oct 31, 2015

Domain: #x in RR#
Range: #F(x) <= 1, in RR#

Explanation:

#F(x) = 1-x^2# is defined for all Real values of #x# and therefore the domain is all Real values (#RR#)

#x^2# has a minimum value of #0# (for #x in RR#)
therefore
#-x^2# has a maximum value of #0#
and
#-x^2+1 = 1-x^2# has a maximum value of #1#.

Therefore #F(x)# has a maximum value of #1#
and the range of #F(x)# is #<= 1#

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