Question

Find the inverse f(x)=x+5/3x-1 f^-1(x)=

Answer 1

Answer:

• f^-1(x) = (3/8)(x +1) . . . . as written
• f^-1(x) = (x +5)/(3x -1) . . . with appropriate parentheses

Step-by-step explanation:

The inverse function can be found by solving for y:

  x = f(y)

  x = y + 5/3y -1 . . . . . . . . . . y +(5/3)y -1 . . . per order of operations

  x+1 = 8/3y . . . . . . . . . . add 1

  (3/8)(x +1) = y . . . . . . . . multiply by 3/8

  f^-1(x) = (3/8)(x +1) . . . . . inverse of the function as written

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Perhaps you intend f(x) = (x+5)/(3x-1). The inverse is found the same way.

  x = (y +5)/(3y -1)

  x(3y -1) = y +5

  3xy -x = y +5 . . . . . eliminate parentheses

  3xy -y = x + 5 . . . . . add x-y

  y(3x -1) = x +5 . . . . . factor out y

  y = (x +5)/(3x -1) . . . divide by the coefficient of y

  f^-1(x) = (x +5)/(3x -1) . . . . inverse of rational function