how do i find the inverse of this function??? show the steps im so confused!?

Question

how do i find the inverse of f(x) = 1/x + 2

show the steps i am so confused on how to get it!

Answer 1

1/f(x) = 1 / [1/x+2]
multiply by x above and below
1/f(x) = x / [ x/x+2x ]
1/f(x) = x / [ 1+2x ]
you can also do a polynomial division ...
divide by 2 above and below
1/f(x) = (1/2) x / [ 1/2+x ]
1/f(x) = (1/2) [ x +1/2-1/2 ] / [ 1/2+x ]
1/f(x) = 1/2 - (1/4) / [ 1/2+x ]
finally 1/f(x) = 1/2 - 1 / [ 2+4x ]

Answer 2

Interchange the x and y. An inverse function is the mirror image of the original function.


y= 1/x + 2

becomes,
x= 1/y + 2

Then rearrange to make it neater, usually they prefer general solutions for final answer.

Answer 3

First, get rid of the fractional term; so you have (1 + 2x)/x.

Then invert f(x) = (1 + 2x)/x by cross multiplying the denominators and numerators.