How do you find (g o f)(x) when f(x)=2xf(x)=2x and g(x)=x^3+x^2+1g(x)=x3+x2+1?

1 Answer
Apr 16, 2018

color(blue)(8x^3+4x^2+1)8x3+4x2+1

Explanation:

(g @ f)(x)=g(f(x))(gf)(x)=g(f(x))

To find the result we substitute x=f(x)x=f(x) in g(x)g(x):

g(x)=x^3+x^2+1g(x)=x3+x2+1

g(f(x))=(f(x))^3+(f(x))^2+1=(2x)^3+(2x)^2+1g(f(x))=(f(x))3+(f(x))2+1=(2x)3+(2x)2+1

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =8x^3+4x^2+1