SOLUTION: Given f(x) below, find f^-1(x). F(x)=-3x+1/x-5 X=/ 5

Question 1149980: Given f(x) below, find f^-1(x).
F(x)=-3x+1/x-5 X=/ 5

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Use parentheses!

The function you show, y = -3x+1/x-5, is -- clearly not what you want.

The function you want is y = (-3x+1)/(x-5), which is

One standard way of finding the inverse of a given function is to switch the x and y and solve for the new y:

[gather all the terms with y on one side]

The inverse is

If you see problems like this often involving inverses of functions like this, note there is a pattern you can use to write the inverse without going through the algebra to find it.

Look at the original function and it inverse:

and

The coefficient of x in the numerator and the constant in the denominator switch places and change sign; the constant in the numerator and the coefficient of x in the denominator remain unchanged.

In general, the inverse of is

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