SOLUTION: the function f(x)= x/3-x find an expression for (f to the negative 1 power) f-1 (x) in addition state the domain of both f and f (-1)

Algebra ->  Functions -> SOLUTION: the function f(x)= x/3-x find an expression for (f to the negative 1 power) f-1 (x) in addition state the domain of both f and f (-1)      Log On


   

Question 34664: the function f(x)= x/3-x find an expression for (f to the negative 1 power) f-1 (x) in addition state the domain of both f and f (-1)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=+x%2F%283-x%29+ --> its domain is any real value of x but not x=3. This is because when x=3, the denominator is then zero and any fraction having a zero denominator gives "ERROR" on your calculator, so HAS TO BE avoided.

Inverse:
+y+=+x%2F%283-x%29+
+y%283-x%29+=+x+
+3y-xy+=+x+
+3y-xy-x+=+0+
+-xy-x+=+-3y+
+-x%28y%2B1%29+=+-3y+
+x%28y%2B1%29+=+3y+
+x+=+%283y%29%2F%28y%2B1%29+

so, here we have +f%28y%29+=+%283y%29%2F%28y%2B1%29+, or seeing as how we usually quote equations in terms of x: +f%28x%29+=+%283x%29%2F%28x%2B1%29+. And as this is the inverse function of the original, then we can say: +f%5E%28-1%29%28x%29+=+%283x%29%2F%28x%2B1%29+

Its domain is: any real value of x but not x=-1 for exactly the same reason as before.

jon