SOLUTION: My teacher likes to throw in a fun problem sometimes to see what we come up. Honestly I am so far behind from being very sick for a week that I don't have the time to play this ga

Algebra ->  Rational-functions -> SOLUTION: My teacher likes to throw in a fun problem sometimes to see what we come up. Honestly I am so far behind from being very sick for a week that I don't have the time to play this ga      Log On


   

Question 1135917: My teacher likes to throw in a fun problem sometimes to see what we come up. Honestly I am so far behind from being very sick for a week that I don't have the time to play this game. Can someone please help me with this? If you have time to show me steps and answers, I would be grateful. This does count for points and I will appreciate anyone willing to assist.
Let f(x) = 4x - 1 and g(x) = x2 + 5.
(a) Find (fog)(x) in general and then find the specific value for (fog)(2).
(b) Find (gof)(x) in general and then find the specific value for (gof)(2).
(c) What can you conclude about (fog)(x) vs. (gof)(x).
(d) Graph all four functions on the same properly labeled coordinate axis.
-----f(x)
-----g(x)
-----(fog)(x)
-----(gof)(x)
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x) = 4x - 1 and g(x) = x2 + 5.

Let f(x) = 4x - 1 and g(x) = x^2 + 5.

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f%28g%28x%29%29=4%28x%5E2%2B5%29-1
4x%5E2%2B20-1
highlight_green%284x%5E2%2B19%29

g%28f%28x%29%29=%284x-1%29%5E2%2B5
16x%5E2-8x%2B1%2B5
highlight_green%2816x%5E2-8x%2B6%29


graph%28400%2C400%2C-12%2C12%2C-3%2C21%2C4x-1%2Cx%5E2%2B5%2C4x%5E2%2B19%2C16x%5E2-8x%2B6%29