SOLUTION: I am having difficulty with inverses of functions: What is the inverse of the following function: {{{f(x)=(4/x)+1}}} Heres what I did: {{{y=(4/x)+1}}} {{{x=(4/y)+1}}} {{{xy

Algebra ->  Rational-functions -> SOLUTION: I am having difficulty with inverses of functions: What is the inverse of the following function: {{{f(x)=(4/x)+1}}} Heres what I did: {{{y=(4/x)+1}}} {{{x=(4/y)+1}}} {{{xy      Log On


   

Question 34348: I am having difficulty with inverses of functions:
What is the inverse of the following function:
f%28x%29=%284%2Fx%29%2B1
Heres what I did:
y=%284%2Fx%29%2B1
x=%284%2Fy%29%2B1
xy=4%2B1
xy=5
y=5%2Fx
When it is checked however, it does not work:
f%281%29=%284%2F1%29%2B1=4%2B1=5
f%5E-1%281%29=5%2F1=5 This check works, but...
f%282%29=%284%2F2%29%2B1=2%2B1=3
f%5E-1%282%29=5%2F2=2.5 This doesn't, I found the graph of the inverse of the function, but I need the equation. Please help!
Thank you,
Sally Mat
Found 2 solutions by Earlsdon, priya:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, you have the right idea but your algebra was a little off!
f%28x%29+=+%284%2Fx%29%2B1
y+=+%284%2Fx%29%2B1 Exchange the x and y and solve for x.
x+=+%284%2Fy%29%2B1 Subtract 1 from both sides.
x-1+=4%2Fy Multiply both sides by y.
y%28x-1%29+=+4 Finally, divide both sides by x-1
y+=+4%2F%28x-1%29
f%5E%28-1%29%2A%28x%29+=+4%2F%28x-1%29 Note! x = 1 not allowed.

Answer by priya(51) About Me  (Show Source):
You can put this solution on YOUR website!
Let Y be f(x)
then the equation becomes,
Y = (4/x )+ 1
Y = (4 + x)/x (taking common divisor on the right side)
now the inverse is given by,
1/Y = x /(4+ x).
check this with x =2,
Y = 2+1 = 3
1/Y = 2/(4+2)
= 1/3
visit my site to learn maths online(mail me if interested!!)
priya