how can i write inverse function ?
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Here is a general method:
1. Replace the variable f(x) with y.
2. Switch the places of x and y.
3. Solve for y.
4. Replace y with f^(–1)(x).
Now applying this method:
y = (2x + 7) / (3x - 1)
x = (2y + 7) / (3y - 1)
x (3y - 1) = 2y + 7
3xy - x = 2y + 7
3xy - 2y = x + 7
y(3x - 2) = x + 7
y = (x + 7) / (3x - 2) and this is the required inverse function so it could be left like this or change the notation to this:
f^(-1) (x) = (x + 7) / (3x - 2)
1. Replace the variable f(x) with y.
2. Switch the places of x and y.
3. Solve for y.
4. Replace y with f^(–1)(x).
Now applying this method:
y = (2x + 7) / (3x - 1)
x = (2y + 7) / (3y - 1)
x (3y - 1) = 2y + 7
3xy - x = 2y + 7
3xy - 2y = x + 7
y(3x - 2) = x + 7
y = (x + 7) / (3x - 2) and this is the required inverse function so it could be left like this or change the notation to this:
f^(-1) (x) = (x + 7) / (3x - 2)
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