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Consider f: R->R given by f(x)=4x+3 . Sh...

Consider `f: R->R` given by `f(x)=4x+3` . Show that `f` is invertible. Find the inverse of `f` .

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In `f: R to R, f(x) = 4x + 3`
Let `x, y in R and f(x) = f(y)`
`rArr 4x + 3 = 4y + 3`
`rArr 4x = 4y rArr x =y `
` therefore f` is one-one.
Again, let `f(x) = y ` where `y in R`
`rArr " " 4x + 3 = y rArr 4x = y - 3 `
`rArr " "x = ( y -3)/( 4) `
Now for each ` y in R, x = (y - 3)/(4) in R ` in such that
`f(x) = f((y -3)/(4))= 4((y-3)/( 4)) + 3 = y`
`therefore f ` is onto.
Therefore, `f` is one-one onto function ` rArr f` is invertible.
`therefore f^(-1) : R to R ` is defined as `f^(-1)(y) = (y-3)/(4)`.
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