Answer:
y = (1-2x)/(3x+6)
Explanation:
To find the inverse of a function, we can swap the x and y variables in the original function and then solve for y. In this case, the original function is f(x) = (1-2x)/(3x+6). Swapping the x and y variables, we get:
y = (1-2x)/(3x+6)
To solve for y, we can first multiply both sides of the equation by (3x+6) to eliminate the fraction:
y(3x+6) = 1-2x
Expanding the left-hand side, we get:
3xy + 6y = 1-2x
Next, we can move all the terms containing y to the left-hand side of the equation and all the other terms to the right-hand side:
3xy + 6y = 1-2x
3xy + 6y - 1 + 2x = 0
Finally, we can divide both sides of the equation by 3 to solve for y:
y(3x+6) - (1-2x)/3 = 0
y = (1-2x)/(3x+6)
Thus, the inverse of the original function f(x) = (1-2x)/(3x+6) is y = (1-2x)/(3x+6).
Tell me if this helped :)