Find the inverse function of
f(x) = (7x-8)/(3x -1).
switch your x and y like
original : y=(7x-8)/(x-1)
to: x=(7y-8)/(y-1) and solve for y.
so: xy-1=7y-8=> xy-7y=-7=> y(x-7)=-7
=> y=-7/(x-7)
x = (7y-8)/(3y-1)
x(3y-1) = 7y-8
3xy-x = 7y-8
y(3x-7) = x-8
y = (x-8)/(3x-7)
To find the inverse function of f(x) = (7x-8)/(3x -1), we can follow these steps:
Step 1: Replace f(x) with y:
y = (7x-8)/(3x - 1)
Step 2: Swap x and y:
x = (7y-8)/(3y - 1)
Step 3: Solve the equation for y:
Multiply both sides by (3y - 1):
x(3y - 1) = 7y - 8
Distribute x:
3xy - x = 7y - 8
Move all terms containing y to one side and all other terms to the other side:
3xy - 7y = x - 8
Factor out y on the left side:
y(3x - 7) = x - 8
Divide both sides by (3x - 7) to isolate y:
y = (x - 8)/(3x - 7)
Step 4: Replace y with f^(-1)(x):
f^(-1)(x) = (x - 8)/(3x - 7)
Therefore, the inverse function of f(x) = (7x-8)/(3x -1) is f^(-1)(x) = (x - 8)/(3x - 7).
To find the inverse function of a given function, we need to follow these steps:
Step 1: Replace f(x) with y.
y = (7x - 8)/(3x - 1).
Step 2: Swap x and y.
x = (7y - 8)/(3y - 1).
Step 3: Solve for y.
Cross-multiply to get rid of the denominators:
x(3y - 1) = 7y - 8.
Distribute the x:
3xy - x = 7y - 8.
Bring all the y terms to one side and all the x terms to the other side:
3xy - 7y = x - 8.
Factor out y on the left side:
y(3x - 7) = x - 8.
Divide both sides by (3x - 7):
y = (x - 8)/(3x - 7).
Step 4: Replace y with f^(-1)(x).
f^(-1)(x) = (x - 8)/(3x - 7).
So, the inverse function of f(x) = (7x - 8)/(3x - 1) is f^(-1)(x) = (x - 8)/(3x - 7).