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Let f(x)= 3x -4/2x+1
Find its inverse f^-1(x).

User Hasiya
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Final answer:

To find the inverse of f(x) = (3x - 4) / (2x + 1), we switch x and y, solve for y, and find f^-1(x) = (-x - 4) / (2x - 3).

Step-by-step explanation:

To find the inverse f^-1(x) of the function f(x) = (3x - 4) / (2x + 1), we must switch the roles of x and y and then solve for y, which will give us the inverse function. Start by replacing f(x) with y:

y = (3x - 4) / (2x + 1)

Now interchange x and y:

x = (3y - 4) / (2y + 1)

Multiply both sides of the equation by (2y + 1) to get rid of the denominator:

x(2y + 1) = 3y - 4

Expand the left side:

2xy + x = 3y - 4

Rearrange the terms to get all terms involving y on one side and the constant term on the other:

2xy - 3y = -x - 4

Factor out y:

y(2x - 3) = -x - 4

Finally, solve for y:

y = (-x - 4) / (2x - 3)

So, the inverse function is f^-1(x) = (-x - 4) / (2x - 3).

User Kangaswad
by
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