1.

If `f:R->R and g:R-> R` are two mappings such that `f(x) = 2x and g(x)=x^2+ 2` then find `fog and gog`.

Answer» (i) (gof) (x) = g [f(x)]
= g (2x) = `(2x)^(2)+2= 4x^(2) + 2.`
and (fog)(x) = f[g(x)]
= `f(x^(2)+2) = 2(x^(2)+2)= 2x^(2) + 4`
`:.` gof `ne` fog. Hence Proved.
(ii) (fog) (2) = f[g(2)]
= f(2^(2) + 2) = f(6) = 12.
(gog)(1) = g [g(1)]
= `g (1^(2)+2) = g (3) = 3^(2) + 2 = 11`.
and (fof) (3) = f[f(3)]
= f`(2xx3) = f(6) = 2xx6 = 12` Ans.


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