Question

FDetermine the inverse function of f(x)= x/x−9.

a) f⁻¹(x)= 9x/x-1
​b) f⁻¹(x)= x/9−x
c) f⁻¹(x)= x/x+9
d) f⁻¹(x)=9x/ x+1

Answer 1

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

Step-by-step explanation:

To find the inverse function of f(x) = x/(x-9), we need to switch the roles of x and y in the equation and solve for y.

Step 1: Write the original equation as y = x/(x-9).

Step 2: Swap x and y to get x = y/(y-9).

Step 3: Solve for y by multiplying both sides of the equation by (y-9). This gives x(y-9) = y.

Step 4: Expand the expression on the left side to get xy - 9x = y.

Step 5: Move the terms with y to one side to get xy - y = 9x.

Step 6: Factor out y on the left side to get y(x-1) = 9x.

Step 7: Divide both sides by (x-1) to isolate y. This gives the inverse function as f⁻¹(x) = 9x/(x-1).