Question

Find t(x) for the given function f(x)=(1)/(6+x)

Answer 1

To find the inverse function of f(x)=(1)/(6+x), swap the variables x and y, solve for y, and express the inverse as t(x)=(1/x)-6.

Step-by-step explanation:

Finding t(x) for the given function f(x)=(1)/(6+x)
To find t(x) for the given function f(x)=(1)/(6+x), we need to understand that t(x) represents the inverse of the function f(x). In other words, we need to find a function that, when composed with f(x), gives us the identity function. Let's proceed with the steps:

1. Start with the function f(x)=(1)/(6+x)
2. Replace f(x) with y to make it easier to work with, so we have y=(1)/(6+x)
3. Swap the variables x and y, so we have x=(1)/(6+y)
4. Solve this equation for y to find the inverse function, so we get y=(1/x)-6

Therefore, the inverse function of f(x)=(1)/(6+x) is t(x)=(1/x)-6.