SOLUTION: h(x)=(6x+1)/(-7-x), find h^-1 find domain find range

Question 531316: h(x)=(6x+1)/(-7-x), find h^-1
find domain
find range
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
h(x)=(6x+1)/(-7-x),
find h^-1
Interchange x and y to get:
x = (6y+1)/(-7-y)
Solve for "y":
-4x - yx = 6y+1
---
6y+1+yx = -4x
y(6+x) = -(4x+1)
y = -(4x+1)/(x + 6)
f^-1(x) = -(4x+1)/(x+6)
-------
find domain
Look for the vertical asymptotes:
Of f(x): All Real Numbers except x = 7
of f(-1): All Real Numbers except x = -6
--------------------
find range
Look for the horizontal asymptotes:
of f(x):All Real Numbers except y = -6
of f^-1(x): All Real Numbers except -2/3
======================================
Cheers,
Stan H.

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