Question

Find domain and range of F(x)=√9-x^2​

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 )