If f(x)= 1/3x and g(x)=3x, then what are g * f (x) and g*f(1/2) 1. 1/x, 2 2. 1/x, 1/2 3. x, 1/2 4. 1/9x, 1/18

The correct answer is:  3)  " x ;  1/2" .

Explanation:

Question 1) 

g [ f(x) ] = ? ;

→ Given:  " f(x) = 1/3 x " ;

→ Given:  " g(x) = 3x " ;  

g [ f(x) ] = g(1/3 x) = 3(1/3 x) = 1x = "x" .

Question 2)

g [ f(1/2) ] = ? ; 

→  Given:  " f(x) = 1/3 x " ;

→  f(1/2) = (1/3) * (1/2) = (1*1) / (3*2) = (1/6) ;

→  g [ f(x) ] =  

          g(1/6) = 3* (1/6) = (3/1) * (1/6) = (3*1) / (1*6) = 3/6 = (3÷3) / (6÷3) = " 1/2 "  .