Question

Find The range of real function defined by f( x ) = √9 − ² ​

Answer 1

Range is the set of all y - values for which the function f ( x ) is defined.

Here f ( x ) are all the y values...let y = f ( x )

=> y = root ( 9 - x^2 )

on squaring both sides

y^2 = 9 - x^2

=> x^2 = 9 - y^2 => x = + - Root ( 9 - y^2 )

Here y takes values between -3 to 3 ( including 3 and -3 also )

Any y value less than - 3 and more than 3 doesnt guve any defined value for the given function...

Thus Range will be [ -3 , 3 ]