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Let f"":""N rarr Y be a function defin...

Let `f"":""N rarr Y` be a function defined as `f""(x)""=""4x""+""3` , where `Y""=""{y in N"":""y""=""4x""+""3` for some `x in N}` . Show that f is invertible and its inverse is
(1) `g(y)=(3y+4)/3`
(2) `g(y)=4+(y+3)/4`
(3) `g(y)=(y+3)/4`
(4) `g(y)=(y-3)/4`

Text Solution

Verified by Experts

`F(x)=4x+3`
`F(x)-3=4x`
`x=(F(x)-3)/4`
`F^-1(x)=(x-3)/4`
`g(y)/N=(y-3)/4`
`y=4x+3`
`g(y)=(y-3)/4`is the answer
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