how to you find a composite function form of y in this problem?
y = 1/[(x^2+3x-5)^3]
I don't understand your question. Composite functions require two functions. You listed one. Please amplify.
That's what I thought at first. But I am thinking I might need to substitute y in place of x and x in place of y?
In order to find the composite function form of y in this problem, you need to consider the substitution you mentioned. Let's start by solving the given equation for x in terms of y.
Starting with the original equation: y = 1/[(x^2+3x-5)^3]
To solve for x, we can start by finding the reciprocal of both sides of the equation:
1/y = (x^2+3x-5)^3
Next, we can take the cube root of both sides:
(1/y)^(1/3) = x^2+3x-5
Now, we have an equation where x is expressed in terms of y. It is not in the form of a composite function yet.
To make it a composite function, we can let y be the input of a function, and then express x as the output of that function.
Let's introduce a new variable, let z = (1/y)^(1/3). Here, z resolves to a new function since y is a variable.
So, z = (1/y)^(1/3)
Now, we can write x in terms of z:
x = z^2 + 3z - 5
Finally, we can express y as a composite function of z:
y = 1/[(x^2+3x-5)^3]
= 1/[(z^2+3z-5)^3]
Therefore, the composite function form of y in this problem is y = 1/[(z^2+3z-5)^3].