Question

Find the Inverse f(x)=4/x+9

Answer 1

The inverse of the function f(x) = 4/x + 9 is found by swapping x and y in the equation and then solving for y. Through a series of algebraic manipulations, the inverse function is determined to be f^-1(x) = 4 / (x - 9). It's important to consider the domain of the original function when working with the inverse.

Step-by-step explanation:

To find the inverse of a function, we need to swap the x and y in the original equation, and then solve for y. Let's work through the steps to find the inverse of the function f(x) = 4/x + 9.

1. Write the original function with y instead of f(x):
   y = 4/x + 9
2. Swap x and y to get the inverse relationship:
   x = 4/y + 9
3. Isolate the y-term on one side of the equation:
   x - 9 = 4/y
4. Multiply both sides by y to get rid of the fraction:
   y(x - 9) = 4
5. Divide both sides by (x - 9) to solve for y:
   y = 4 / (x - 9)

The inverse function is f-1(x) = 4 / (x - 9).

Note that the domain of the original function excludes x = 0, as that would make the denominator zero. Similarly, the inverse function's domain excludes x = 9, for the same reason.