find (FxG)(X) and (GxF)(X) when f(x)=5x^2-1 and g(x)=2/x
f(g(x))=5(2/x)^2-1 put g in for x
=5(4/x)-1 Exponents
=(20/x)-1 This is it or get
= (20/x)-(x/x) LCD
= (20-x)/x
Solution: (20/x)-1 OR (20-x)/x
g(f(x))=2/(5x^2-1) put f in for g
This is simplified
To find (FxG)(x), you need to multiply f(x) and g(x) as follows:
(FxG)(x) = f(x) * g(x)
Given that f(x) = 5x^2 - 1 and g(x) = 2/x, we can substitute these values into the equation:
(FxG)(x) = (5x^2 - 1) * (2/x)
To simplify this expression, we can distribute the multiplication:
(FxG)(x) = 5x^2 * 2/x - 1 * 2/x
Next, simplify each term separately:
(FxG)(x) = 10x - 2/x
Therefore, (FxG)(x) = 10x - 2/x.
Now, let's find (GxF)(x), which is the multiplication of g(x) and f(x):
(GxF)(x) = g(x) * f(x)
Using the given functions g(x) = 2/x and f(x) = 5x^2 - 1:
(GxF)(x) = (2/x) * (5x^2 - 1)
Distribute the multiplication:
(GxF)(x) = 2/x * 5x^2 - 2/x * 1
Simplifying each term:
(GxF)(x) = 10x - 2/x
Notice that this result is the same as (FxG)(x). Therefore, (GxF)(x) = 10x - 2/x.