SOLUTION: Find the inverse of the function. f(x) = (x - 4)/(x + 4) x does not equal -4

Algebra ->  Inverses -> SOLUTION: Find the inverse of the function. f(x) = (x - 4)/(x + 4) x does not equal -4      Log On


   

Question 928716: Find the inverse of the function.
f(x) = (x - 4)/(x + 4) x does not equal -4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%28x+-+4%29%2F%28x+%2B+4%29
to find the inverse of the function, swap x and y

f%28x%29+=+%28x+-4%29%2F%28x+%2B+4%29...since f%28x%29+=y

y=+%28x+-4%29%2F%28x+%2B+4%29
x=+%28y+-4%29%2F%28y+%2B+4%29.....solve for y
x%28y+%2B+4%29=+%28y+-4%29
xy+%2B+4x=+y-4
4%2B+4x=+y-xy
4%281%2Bx%29=+y%281-x%29
y=4%281%2Bx%29%2F%281-x%29
y=4%281%2Bx%29%2F%28-%28x-1%29%29
y=-4%281%2Bx%29%2F%28x-1%29
or
f%5E-1%28x%29=-4%281%2Bx%29%2F%28x-1%29