Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = eight divided by x squared + 2
if y = 8/(x^2+2)
Then one choice is clearly
f(x) = 8/x
g(x) = x^2+2
If y = 8/x^2 + 2, then we have
f(x) = x+2
g(x) = 8/x^2
Well, it seems like we have an interesting function here, so let's break it down.
First, let's define g(x) as x^2 + 2. This means that we can replace x^2 + 2 in the original equation to get y = 8 divided by g(x).
Now, let's define f(x) as 8 divided by x. This means that we can replace 8 divided by g(x) with f(g(x)), giving us y = f(g(x)).
So, f(x) = 8 divided by x and g(x) = x^2 + 2.
Put it all together, and we have y = f(g(x)), which can be described as y = 8 divided by (x^2 + 2).
Now, I know math can be puzzling sometimes, but hey, at least this function has got its own little bot-approved explanation.
To find f(x) and g(x) such that y = f(g(x)), we can break down the given function into two parts. Let's start by expressing the function y = eight divided by x squared + 2 as a composition of two functions.
Let g(x) = x^2 + 2. We choose this function to represent the denominator of the original expression.
Now, let's find f(x) such that f(g(x)) = y. We want f(g(x)) to represent the numerator, which is 8.
We can express f(x) as f(x) = 8 / x. This function will provide the desired numerator.
Therefore, the function y = eight divided by x squared + 2 can be described as y = f(g(x)), where f(x) = 8 / x and g(x) = x^2 + 2.
To find the functions f(x) and g(x) that would describe the given function as y = f(g(x)), we need to break down the equation y = eight divided by x squared + 2 into two parts.
Let's denote g(x) as the expression in the denominator of the given equation: x squared + 2. So g(x) = x^2 + 2.
Next, we can denote f(x) as the expression in the numerator of the given equation: eight divided by g(x). So f(x) = 8/g(x).
Therefore, the functions f(x) and g(x) that describe the equation y = eight divided by x squared + 2 are:
f(x) = 8/(x^2 + 2)
g(x) = x^2 + 2