I have two questions:
Find (f *g)(x) when f(x)= (sqrt x+3)/x and g(x)=(sqrt x+3)/2x
Determine the doamin of (f/g)(x) when f(x)= -1/x and g(x)= (sqrt 3x-9)
+23251 Find (f*g)(x) when f(x) = [ sqrt(x + 3) ] / x and g(x) = [ sqrt(x + 3) ] / (2x)
(f*g)(x) = f(x) * g(x) = { [ sqrt(x + 3) ] / x } * { [ sqrt(x + 3) ] / (2x) }
= [ sqrt(x + 3) * sqrt(x + 3) ] / [ x * 2x ]
= (x + 3) / ( 2x2 )
Determine the domain of (f/g)(x) when f(x) = -1/x and g(x) = sqrt(3x - 9)
(f/g)(x) = f(x) / g(x) = [ -1/x ] / [ sqrt(3x - 9) ] = -1 / [ x * sqrt(3x - 9) ]
Two restrictions:
Since x is in the denominator x can't be zero.
Since 3x - 9 is under the square root sign, 3x - 9 >= 0 ---> 3x >= 9 ---> x >= 3.
Combining these two restrictions, x >= 3.
