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Let f be any real function and let g ...

Let `f` be any real function and let `g` be a function given by `g(x)=2x` . Prove that `gof=f+f` .

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`f: Rto R ldots ldots . . `[ Given ]
Since, `g(x)=2 x is a polynomial, g: R to R`
Clearly, `g o f: R to R and f+f: R to R`
So, domains of g o f and f+f are the same.
` Rightarrow(g o f)(x) =g[f(x)] `
` =2 f(x) ldots ldots ldots[ Since, g(x)=2 x] `
` ...
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