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.

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) (Show Source): You can put this solution on YOUR website!
Start with the given function. The domain here is that "x" can be any real number except

Replace f(x) with y

Swap x and y

Multiply both sides by y-2

Distribute

Add to both sides.

Subtract from both sides.

Rearrange the terms.

Factor out the GCF "y"

Divide both sides by x-5

So the inverse function is . The domain here is that "x" can be any real number except
Answer by RAY100(1637) (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
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