Given the function Find the inverse of gx use parenthesis to

Given the function

Find the inverse of g(x) (use parenthesis to type your answer)

[inv]

Solution

Given that

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

let g (x) = y

Then

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

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

4xy + 3y = 1 - 2x

4xy + 2x = 1 - 3y

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

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

And then switch the x\'s and y\'s

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

Therefore,

y is inverse functon

y = g^-1 (x)

Therefore,

The inverse function of g (x) is g^-1 (x)

Hence,

  g^-1 (x) = (1-3x) / (4x +2 )