Question

A function is defined by f ( x ) = 3−xx , where x ≠ 0. Find f - 1 ( x )

Answer 1

To find the inverse function of f(x) = 3 - x/x, interchange x and y, solve for y, and rewrite the equation in terms of y. The inverse function is f^(-1)(x) = 3/(x + 1).

Step-by-step explanation:

f(x) = 3 - x/x

To find the inverse function, interchange x and y in the original function and solve for y:

x = 3 - y/y

Rewrite the equation in terms of y:

yx = 3 - y

Add y to both sides:

yx + y = 3

Factor out y:

y(x + 1) = 3

Divide both sides by (x + 1):

y = 3/(x + 1)

Therefore, the inverse function is f-1(x) = 3/(x + 1).