The function f is defined as f(x)=(2x+1)/(x-3). Find the value of k so that the inverse of f is f^-1(x)=(3x+1)/(x-k).

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll determine the inverse function f^-1(x).

Let f(x)=y, such as:

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

We'll multiply both sides by (x-3):

xy - 3y = 2x+1

We'll move 3y to the right:

xy = 2x + 3y +1

We'll subtract 2x both sides:

xy - 2x = 3y + 1

We'll factorize by x to the left:

x(y - 2) = 3y + 1

We'll divide by (y-2):

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

The inverse function is: f^-1(x) = (3x+1)/(x-2)

Comparing with the given expression of f^-1(x) = (3x+1)/(x-k), we'll identify k = 2.