SOLUTION: Find the inverse function of f. State the domain and range of f. f(x) = (3x-2)/(x+5)

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Question 60237: Find the inverse function of f. State the domain and range of f.
f(x) = (3x-2)/(x+5)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse function of f. State the domain and range of f.
f%28x%29=%283x-2%29%2F%28x%2B5%29 The demoninator cannot = 0, so x+5 cannot =0, x cannot =-5. Therefore the domain is that x is all real numbers except -5.
To find the inverse, let f(x)=y
y=%283x-2%29%2F%28x%2B5%29 Now switch your x and y and solve for y.
x=%283y-2%29%2F%28y%2B5%29
x%28y%2B5%29=%283y-2%29%28y%2B5%29%2F%28y%2B5%29
xy%2B5x=%283y-2%29%2Across%28y%2B5%29%2Fcross%28y%2B5%29
xy%2B5x=3y-2
xy-3y%2B5x=3y-3y-2
xy-3y%2B5x-5x=-5x-2
y%28x-3%29=-5x-2
y%28x-3%29%2F%28x-3%29=%28-5x-2%29%2F%28x-3%29
y%2Across%28x-3%29%2Fcross%28x-3%29=%28-5x-2%29%2F%28x-3%29
y=%28-5x-2%29%2F%28x-3%29
f^(-1)(x)=%28-5x-2%29%2F%28x-3%29 <-- this is the inverse function.
The range is anything that doesn't make the inverse undefined: y can be all real numbers except y cannot = 3.
Happy Calculating!!!