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Let f: R-R be a function given by f(x)=a...

Let `f: R-R` be a function given by `f(x)=a x+b` for all `x in R` . Find the constants a and b such that `fof=I_Rdot`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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  2. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

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  3. Let f: R-R be a function given by f(x)=a x+b for all x in R . Find th...

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  4. If f(x)=e^x and g(x)=(log)e x(x >0), find foga n dgofdot Is fog=gof?

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  5. If f:[0,oo)vecRa n dg: RvecR be defined as f(x)=sqrt(x) and g(x)=-x^2-...

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  6. Let f and g be real functions defined by f(x)=x/(x+1) a n d g(x)=1/(x...

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  7. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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  8. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

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

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

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  11. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4)=1, then (gof)...

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

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  13. Let A={a,b,c,d} and f :A->A be given by f={(a,b),(b,d),(c,a),(d,c)} , ...

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  14. Let f={(3,1),(9,3),(12 ,4)} and g={(1,3),(3,3),(4,9),(5,9)}dot Show th...

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  15. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

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  16. Let f: RrarrR and g: RrarrR be two functions such that fog(x)=sinx^2...

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  17. Let R be the set of real numbes. If f: RvecR ;f(x)=x^2 and g: RvecR ;g...

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  18. If f(x)=-4-(x-7)^3 , write f^(-1)(x)dot

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  19. If f:{5,6}vec{2,3}a n dg:{2,3},vec{5,6} are given by f={(5,2),(6,3)} a...

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  20. If a function g={(1,1),(2,3),(3,5),(4,7)} is described by g(x)=alphax+...

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