SOLUTION: This problem has been bothering me for a while now. I need help on how to solve it. It goes like this: If f(x)= 1-3x and g(x)= 1/ x^2 +1, find f(g(0)) and g(f(1))

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: This problem has been bothering me for a while now. I need help on how to solve it. It goes like this: If f(x)= 1-3x and g(x)= 1/ x^2 +1, find f(g(0)) and g(f(1))      Log On

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Question 87821: This problem has been bothering me for a while now. I need help on how to solve it. It goes like this: If f(x)= 1-3x and g(x)= 1/ x^2 +1, find f(g(0)) and g(f(1))
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=+1-3x+ and +g%28x%29=+1%2F%28x%5E2%2B1%29+

fg(0) says wherevere x is, put zero as its value --> in the g(x) function. So:

+g%28x%29=+1%2F%28x%5E2%2B1%29+ becomes
+g%280%29=+1%2F%28%280%29%5E2%2B1%29+
+g%280%29=+1%2F%280%2B1%29+
+g%280%29=+1%2F1+
+g%280%29=+1+

Now put this value into f(x):
+f%28x%29=+1-3x+ becomes
+f%281%29=+1-3%281%29+
+f%281%29=+1-3+
+f%281%29=+-2+

Now lets work out gf(1). This says to put 1 into f(x) for x. Work out the answer and then put that answer into g(x).

+f%28x%29=+1-3x+ becomes
+f%281%29=+1-3%281%29+
+f%281%29=+1-3+
+f%281%29=+-2+

then
+g%28-2%29=+1%2F%28%28-2%29%5E2%2B1%29+ becomes
+g%28-2%29=+1%2F%284%2B1%29+
+g%28-2%29=+1%2F5+

Does this help. Do you understand any better? Read my tutorial on functions - it hopefully explains things in more depth.

cheers
jon