Question

If f(x)=(2x+1)/x find f^-1(x)

Answer 1

To find the inverse function, we interchange x and y, solve for y, and express y in terms of x. Hence, f^-1(x) is equal to 1/(x - 2).

Step-by-step explanation:

1. First, we substitute y for f(x), so the equation becomes y = (2x + 1)/x.
2. Next, we interchange x and y to obtain x = (2y + 1)/y.
3. To find the inverse, we solve for y: xy = 2y + 1. Distribute xy to get xy = 2y + 1.
4. Now, isolate y by subtracting 2y from both sides: xy - 2y = 1.
5. Factor out y: y(x - 2) = 1.
6. Divide both sides by (x - 2) to solve for y: y = 1/(x - 2).
7. Therefore, the inverse function is f^-1(x) = 1/(x - 2).

Answer 2

f^-1 x = 1 / (x - 2).

Step-by-step explanation:

Let y = (2x + 1)/x

Find x in terms of y:

xy = 2x + 1

xy - 2x = 1

x(y - 2) = 1

x = 1 / (y - 2)

So f^-1 x = 1 / (x - 2).