Question

Let f(x) = √x and g(x) = x be two functions over the set of negative real numbers. Find (f+g)x ,(f-g)x , (fg)x , (f/g)x .

Answer 1

$RELATIONS \: \: AND \: \: FUNCTIONS \\ \\ \\ We \: have \: , \: \\ \\ \\ (f+g)(x ) \: = \: \sqrt{x} + x \\ \\ \\ (f - g)(x ) \: = \: \sqrt{x} - x \\ \\ \\ (fg)(x) = \sqrt{x} (x) = {x}^{ \frac{3}{2} } \\ \\ \\ (\frac{f}{g} )(x) = \frac{ \sqrt{x} }{x} = {x}^{ \frac{ - 1}{ \: \: \: 2} } \: \: \: \: \: \: \: \: \: Ans.$