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If the function* f* : R → R be given by *f*[*x*] = *x*^{2} + 2 and *g* : R → R be given by `g(x)=x/(x−1)` , x≠1, find fog and gof and hence find fog (2) and gof (−3).

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#### Solution

Here, *f*[*x*] = *x*^{2} + 2 and g(x)=x/(x−1), x≠1

∴ fog (x)=g^{2}(x)+2

`⇒fog(x)=x^2/(x−1)^2+2`

`⇒fog (x)=(x^2+2(x−1)^2)/(x−1)^2`

Now, `fog (2)=(2^2+2(2 − 1)^2)/(2−1)^2=(4+2)/1=6`

Similarly, `gof (x)=(x^2+2)/(x^2+2−1)=(x^2+2)/(x^2+1)`

`⇒gof (−3)=((−3)^2+2)/((−3)^2+1)=11/10`

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