If f(x) = 3x , g(x) = x² then find
fog,gof,gog,fof
To find fog, substitute g(x) into f(x):
fog(x) = f(g(x)) = f(x^2) = 3(x^2) = 3x^2.
To find gof, substitute f(x) into g(x):
gof(x) = g(f(x)) = g(3x) = (3x)^2 = 9x^2.
To find gog, substitute g(x) into g(x):
gog(x) = g(g(x)) = g(x^2) = (x^2)^2 = x^4.
To find fof, substitute f(x) into f(x):
fof(x) = f(f(x)) = f(3x) = 3(3x) = 9x.
To find f o g (f composite g), we substitute g(x) into f(x):
f o g = f(g(x)) = f(x²) = 3(x²) = 3x²
To find g o f (g composite f), we substitute f(x) into g(x):
g o f = g(f(x)) = g(3x) = (3x)² = 9x²
To find g o g (g composite g), we substitute g(x) into g(x):
g o g = g(g(x)) = g(x²) = (x²)² = x^4
To find f o f (f composite f), we substitute f(x) into f(x):
f o f = f(f(x)) = f(3x) = 3(3x) = 9x
Therefore, f o g = 3x², g o f = 9x², g o g = x^4, and f o f = 9x.