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