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Let f(x)=x^2+x+1 and g(x)=sinx . Show th...

Let `f(x)=x^2+x+1` and `g(x)=sinx` . Show that `fog!=gof` .

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Statement-1: If f:R to R and g:R to R be two functions such that f(x)=x^(2) and g(x)=x^(3) , then fog (x)=gof (x). Statement-2: The composition of functions is commulative.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Find fog and gof , if f(x)=c ,\ c in R , g(x)=sinx^2

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  2. Find fog and gof , if f(x)=x^2+2 , g(x)=1-1/(1-x)

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  3. Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .

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  4. L e tf: R->R :f(x)=|x|, Prove that fof=f

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  5. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  6. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  7. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  8. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  9. If f(x)=sinx and g(x)=2x be two real functions, then describe gof a...

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  10. Let f,\ g,\ h be real functions given by f(x)=sinx , g(x)=2x and h(...

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  11. Let f be any real function and let g be a function given by g(x)=2x...

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  12. If f(x)=sqrt(1-x) and g(x)=(log)e x are two real functions, then de...

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  13. If f:(-pi//2,pi//2)->R and g:[-1,\ 1]->R be defined as f(x)=tanx and g...

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  14. If f(x)=sqrt(x+3) and g(x)=x^2+1 be two real functions, then find f...

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  15. Let f be a real function given by f(x)=sqrt(x-2) . Find fofdot Also...

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  16. Let f(x)=1+x, 0 leq x leq 2 and f(x)=3−x,2 lt x leq 3. Find f(f(x)).

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  17. If f, g,: R- R be two functions defined as f(x)=|x|+x and g(x)=|x|-x...

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  18. If f: Q->Q is given by f(x)=x^2 , then find f^(-1)(9)

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  19. If f: Q->Q is given by f(x)=x^2 , then find f^(-1)(5)

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  20. If f: Q->Q is given by f(x)=x^2 , then find f^(-1)(0)

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