Given the function f(x)=(6)/(x+4)find a formula for the inverse function
I say it is f^-1 (x)=(6)/(x-4)
y = 6/(x+4)
x = 6/(y+4)
x y + 4x = 6
x y = 6-4x
y = (6-4x)/x
So what would this = ?
What i said? f^-1(x)(6) over (x - 4)
To find the inverse function, we need to switch the roles of x and y in the original function and solve for y.
Let's start by rewriting the original function as:
y = f(x) = 6/(x + 4)
Now, swap x and y:
x = 6/(y + 4)
Next, solve for y:
xy + 4x = 6
xy = 6 - 4x
y = (6 - 4x)/x
This is the inverse function of f(x). So, the formula for the inverse function is:
f^(-1) (x) = (6 - 4x)/x