find (FxG)(X) and (GxF)(X) when f(x)=5x^2-1 and g(x)=2/x
fxg= 5(2/x)^2-1=20/x^2 -1
To find (FxG)(X), we need to multiply f(x) and g(x) and substitute X for x.
Given f(x) = 5x^2 - 1 and g(x) = 2/x, we have:
(FxG)(X) = (5X^2 - 1) * (2/X)
To simplify this expression, we can follow these steps:
Step 1: Distribute:
(FxG)(X) = (5X^2 - 1) * (2/X)
= (10X^2 - 2) / X
Thus, (FxG)(X) simplifies to (10X^2 - 2) / X.
Now, let's find (GxF)(X). This time we'll multiply g(x) and f(x) and substitute X for x.
Given f(x) = 5x^2 - 1 and g(x) = 2/x, we have:
(GxF)(X) = (2/X) * (5X^2 - 1)
To simplify this expression, we can follow these steps:
Step 1: Distribute:
(GxF)(X) = (2/X) * (5X^2 - 1)
= (10X^2 - 2) / X
Thus, (GxF)(X) simplifies to (10X^2 - 2) / X.
We can see that (FxG)(X) and (GxF)(X) yield the same result: (10X^2 - 2) / X.