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If f(x)=sinx and g(x)=2x be two real fun...

If `f(x)=sinx` and `g(x)=2x` be two real functions, then describe `gof` and `fogdot` Are these equal functions?

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Verified by Experts

Given as `f(x)=sin x and g(x)=2 x`
We know
` {f:} {R} to[-1,1] and g: R to R`
Clearly, the range of f is a subset of the domain of g.
` gof: R to R`
` (g o F)(x)=g(f(x))`
` =g(sin x)`
` =2 sin x`
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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

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

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

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

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

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

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

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

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

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

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  12. If f: Q->Q is given by f(x)=x^2 , then find f^(-1)(-25)

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

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  14. If the function f: R->R be defined by f(x)=x^2+5x+9 , find f^(-1)(8) a...

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  15. If the function f: C->C be defined by f(x)=x^2-1 , find f^(-1)(9) and ...

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  16. Let f: R->R be defined as f(x)=x^2+1 . Find: f^(-1)(10)

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  17. If A={0,\1,\ 2,\ 3,} , B={1,\ 3,\ 5,\ 7,\9} and f: A->B is given by f(...

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  18. Let S = {1, 2, 3}. Determine whether the functions f : S->Sdefined as ...

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  19. Consider f : {1, 2, 3}->{a , b , c}given by f(1) = a, f(2) = band f(3)...

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  20. If f: Rvec is defined by f(x)=2x+7. Prove that f is a bijection. Also,...

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