SOLUTION: functions f and g are defined as follows: f(x)=x^5 and g(x()= 1/x+1 Evaluate f(2), f(-1), g(0). write down f(g(x)) and g(f(x)) as functions of x

Algebra ->  College  -> Linear Algebra -> SOLUTION: functions f and g are defined as follows: f(x)=x^5 and g(x()= 1/x+1 Evaluate f(2), f(-1), g(0). write down f(g(x)) and g(f(x)) as functions of x      Log On


   

Question 1012368: functions f and g are defined as follows:

f(x)=x^5 and g(x()= 1/x+1

Evaluate f(2), f(-1), g(0).

write down f(g(x)) and g(f(x)) as functions of x
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x%5E5

when x = 2, you replace x with 2 to get f(2) = 2%5E5 = 32

when x = -1, you replace x with -1 to get f(-1) = %28-1%29%5E5= -1

g(x) = 1%2F%28x%2B1%29

when x = 0, you replace x with 0 to get g(0) = 1%2F%280%2B1%29 = 1/1 = 1

f(x) = x%5E5

g(x) = 1%2F%28x%2B1%29

f(g(x)) means you replace x with g(x) to get f(g(x)) = %28g%28x%29%29%5E5.

since g(x) = 1%2F%28x%2B1%29, then you replace g(x) with 1%2F%28x%2B1%29 to get f(g(x)) = %281%2F%28x%2B1%29%29%5E5.

therefore f(g(x)) = %281%2F%28x%2B1%29%29%5E5 when f(x) = x%5E5 and g(x) = 1%2F%28x%2B1%29.

g(f(x)) means you replace x with f(x) to get g(f(x)) = 1%2F%28f%28x%29%2B1%29.

since f(x) = x%5E5, then you replace f(x) with x%5E5 to get g(f(x)) = 1%2F%28x%5E5%2B1%29.

therefore g(f(x)) = 1%2F%28x%5E5%2B1%29 when g(x) = 1%2F%28x%2B1%29 and f(x) = x%5E5.