Ok, so I'm trying to find the inverse of each function. We're learning about Inverse Functions and Relations.
The problem is f(x)=sqr.root of x/6
The sqr root is confusing me.
To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we want to find an equation of the form y = f^(-1)(x), where f^(-1) denotes the inverse of f.
Let's start by rewriting the given function:
f(x) = √(x/6)
To switch the roles of x and y, we can rewrite the equation as follows:
x = √(y/6)
Now, we need to solve for y. To eliminate the square root, we can square both sides of the equation:
x^2 = (√(y/6))^2
x^2 = y/6
To isolate y, we can multiply both sides of the equation by 6:
6x^2 = y
Therefore, the inverse of the function f(x) = √(x/6) is f^(-1)(x) = 6x^2.
Please note that taking the square root of both sides and squaring both sides may introduce extraneous solutions. Therefore, it's important to check whether the inverse function obtained satisfies all the necessary conditions, such as the domain and range of the original function.