SOLUTION: If f(x) = (5x-3)/(x-2) Find the inverse function of f. would that be just the opposite? = (x-2)/(5x-3)? State the domain of f. State the domain of the inverse function.

Algebra ->  Average -> SOLUTION: If f(x) = (5x-3)/(x-2) Find the inverse function of f. would that be just the opposite? = (x-2)/(5x-3)? State the domain of f. State the domain of the inverse function.       Log On


   

Question 192120: If f(x) = (5x-3)/(x-2)
Find the inverse function of f. would that be just the opposite? = (x-2)/(5x-3)?
State the domain of f. State the domain of the inverse function.
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%285x-3%29%2F%28x-2%29 Start with the given function. The domain here is that "x" can be any real number except x%3C%3E2


y+=+%285x-3%29%2F%28x-2%29 Replace f(x) with y


x+=+%285y-3%29%2F%28y-2%29 Swap x and y


x%28y-2%29+=+5y-3 Multiply both sides by y-2


xy-2x+=+5y-3 Distribute


xy=5y-3%2B2x Add 2x to both sides.


xy-5y=-3%2B2x Subtract 5y from both sides.


xy-5y=2x-3 Rearrange the terms.


y%28x-5%29=2x-3 Factor out the GCF "y"


y=%282x-3%29%2F%28x-5%29 Divide both sides by x-5



So the inverse function is . The domain here is that "x" can be any real number except x%3C%3E5

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
INVERSE of a number is reciprocal, ie 2, inv 2 = 1/2
however inverse of FUNCTION indicates a function that is reflected over y=x
Normally this is solved by substituting x for y ,,,, and y for x
f(x) =(5x-3) / (x-2)
but f(x) =y
y = (5x-3) / (x-2) DOMAIN is all REAL numbers except x=2
inverting
x = (5y-3) / (y-2)
or (y-2) = (5y-3) /x Domain is all REAL numbers except x=0