Perform the indicated operation - Show Work Please

Question

f(x) = x^2+2x

g(x) = 3x + 1

 

Find f(g(x))

 

Final Answer is meant to be 9x^2 + 12x + 3

Answer 1

f(x) = x²+2x
g(x) = 3x + 1

 

For f(g(x)), simply replace to x in f(x) with g(x), as follows:

 

f(x) = x²+2x

f(g(x)) = g(x)² + 2g(x)

 

Now replace the g(x) with 3x+1:

 

f(g(x)) = (3x+1)² + 2(3x+1)

f(g(x)) = 9x² + 6x + 1 + 6x + 2

f(g(x)) = 9x² + 12x + 3