Given the functions fx3x2 gx42x Find a fgx b gf0Solutionf x

Given the functions f(x)=3x+2, g(x)=4-2x   

Find (a) (f+g)(x)=  

(b) (g/f)(0)=

Solution

f (x) = 3x + 2 and g (x) = 4 - 2x.

Therefore (f +g) (x) = f (x) + g (x) = 3x + 2 + ( 4 -2x) = x + 6

Also (g /f) (x) = g (x)/ f (x) = ( 4 - 2x)/ ( 3x+ 2). Therefore (g /f) ( 0 ) = ( 4 -0)/ (0 + 2) = 4/2 = 2