Find (fog)(x)and (gof)(x)if f(x)=x-x^2 and g(x)= 2x+3.
Okay so I did the following:
For f(of)g(x), take (2x+3) - (2x+3)^2
(insert g(x) where the "x" is in f(x) )
For g(of)f(x), take 2[x-x^2] +3
The first answer that I get for (2x+3) - (2x+3)^2 is -4x^2-12x-9
The second answer that I get for
2[x-x^2] +3 is 2x-2x^2+3
are these the answers to the problem?
You did not subtract the terms correctly for f(of)g(x). You only did the (2x+3)^2 calculation.
Your g of f(x) is correct
for f of g(x) I have -4x^2-10x-6
Is this right?
To find (fog)(x), we substitute g(x) into f(x), resulting in f(g(x)):
f(g(x)) = f(2x+3) = (2x+3) - (2x+3)^2.
To find (gof)(x), we substitute f(x) into g(x), resulting in g(f(x)):
g(f(x)) = g(x-x^2) = 2(x-x^2) + 3.
Let's evaluate these expressions:
For (fog)(x):
f(g(x)) = (2x+3) - (2x+3)^2
= (2x+3) - (4x^2+12x+9)
= -4x^2-10x-6.
For (gof)(x):
g(f(x)) = 2(x-x^2) + 3
= 2x-2x^2+3.
So, the correct answers are:
(fog)(x) = -4x^2-10x-6,
(gof)(x) = 2x-2x^2+3.
Note: It seems like there was an error in the calculations you provided in your question. The correct expressions for (fog)(x) and (gof)(x) are as mentioned above.