Question

Inverse Rational Function: g(x)=6x-1/4x+7

Answer 1

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Answer:

  g^-1(x) = (7x+1)/(6 -4x)

Step-by-step explanation:

Substitute y for x and solve for y.

  g(y) = x

  (6y -1)/(4y +7) = x

  6y -1 = x(4y +7) . . . . multiply by 4y+7

  6y -4xy = 7x +1 . . . . add 1-4xy

  y(6 -4x) = 7x +1 . . . . factor out y

  y = (7x +1)/(6 -4x) . . . divide by the coefficient of x

  $\boxed{g^{-1}(x)=\dfrac{7x+1}{6-4x}}$