Question

① Find the domain & range of the following real function ,1. f (x) =|x|
f(x)=√9-x2​

Answer 1

Answer:

values of x will be restricted such that ( 9 - x^2 ) > 0

9 - x^2 = ( 3 + x ) ( 3 - x )

this is parabola of inverted U shape, whose value is +ve in between roots.

so ( 9 - x^2 ) > 0 for x in between -3 & 3

so domain is x = [ -3 , 3 ]

range = ( 0 , max of f(x) )

f(x) is maximum at mid point of roots, i.e. f max = f(0) = 3

so range = ( 0 , 3 )

Answer 2

Answer:

Domain and range

f(x)=

9−x

2

y=

9−x

2

9−x

2

≥0

9−x

2

≥0

x

2

≤9

x≤

−

+

3

x∈[−3,3]

y

2

=9−x

2

x

2

=9−y

2

x=

9−y

2

9−y

2

≥0

y

2

≤9y∈3,−3

y=+ve

∵y∈[0,3]