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

1 Answer
Somebody N.
Apr 16, 2018

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

Explanation:

#(g @ f)(x)=g(f(x))#

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

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

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

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

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