find inverse of the funcion `f(x) = (8/3)x – (2/3)`

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find inverse of the funcion `f(x) = (8/3)x – (2/3)`

Postby barnamah » Thu 31 March, 2011 22:01

find inverse of the function `f(x) = (8/3)x – (2/3)`
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Re: find inverse of the funcion `f(x) = (8/3)x – (2/3)`

Postby Integr88 » Thu 31 March, 2011 22:10

to inf the inverse of a function such as `y=8/3x – 2/3` we first solve for x


`y=(8/3)x – (2/3)` as we see `1/3` is common in both terms so factor it out
`y=1/3(8x-2)`

Multiply both side by 3 and we have:
`y*3=3*1/3(8x-2)` 3 on the right side cancels out and we have:

`3y=8x-2` now add 2 to both side of equation and we have:

`3y+2=8x-2+2`
`3y+2=8x`

We now get rid of x by multiplying both side of equation by `1/8` so the equation will look `(3y+2)*1/8=8x*1/8` and we have:
`(3y+2)/8=x`

now we replace x with y and we have: `(3x+2)/8=y`

we further simplify as `y=3/8x+2/8`

`:.` final inverse function is `y=3/8x+2/8`
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