find fgx gfx with fx 3x5 and gx x2 11Solutionfx 3x5 and gx x

find f(g(x)), g(f(x)) with f(x)= 3x-5 and g(x) =x² +11

Solution

f(x)= 3x-5 and g(x) =x² +11

a) f(g(x)) ;To find f(g(x)) plug x= g(x) in f(x)

f(g(x)) = 3(x^2 +11) -5 = 3x^2 + 28

b) g(f(x))

plug x= f(x) in g(x)

g(f(x)) = (3x-5)^2 +11 = 9x^2 +25 -30x +11

= 9x^2 -30x +36