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Let f: R ->Rbe defined as f(x) = 10 x +...

Let `f: R ->R`be defined as `f(x) = 10 x + 7`. Find the function `g: R ->R`such that`gof=fog=1_R`

Text Solution

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In `F: R rarr R`, f(x) = 10 x +7
Let x,y `in`R
and f(x)=f(y)
`rArr 10 x +7 =10 y +7`
`rArr 10x = 10 y `
`rArr x=y`
`therefore` f is one - one
Again let f(x) =y where `y in R`
`rArr 10x +7 =y rArr x(y-7)/(10)i R`
`therefore` f is onto
Now `(fog )(x) = f((y-7)/(7))`
`=10 ((y-7)/(10))+7=y`
`therefore go f =I_R "and" fog =I_R`
`therefore g: R rarr R ` is defined as g(y) `=(y-7)/(10)`
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Let f:R rarr R be defined as f(x)=10x+7 Find the function g:R rarr R such that gof=fog=I_(R)

Let f:R rarr R be defined as f(x)=10x+7 Find the function such that gof=fog=1_(R)

Knowledge Check

  • The function f: R to R defined by f(x) = 4x + 7 is

    A
    one-one
    B
    onto
    C
    into
    D
    bijective

  • Let function f : R to R be defined by f (x) = 2x + sin x for x in R Then f is

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    one-to-one and onto
    B
    one-to-one but NOT onto
    C
    onto but NOT one-to-one
    D
    neither one-to-one nor onto

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