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If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are ...

If `f(x)=sqrtx(x > 0) and g(x)=x^2-1` are two real functions, find `fog and gof` is `fog=gof ?`

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To solve the problem, we need to find the compositions \( f(g(x)) \) and \( g(f(x)) \), and then check if they are equal. ### Step 1: Find \( f(g(x)) \) Given: - \( f(x) = \sqrt{x} \) for \( x > 0 \) - \( g(x) = x^2 - 1 \) ...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let f:R→R and g:R→R defined by f(x)=x 2 and g(x)=(x+1). Show that g...

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

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

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

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  5. If f: Rvec is defined by f(x) = 3x – 5 Prove that f is a bijection. Al...

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

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  7. 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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  8. Let f,g: RvecR be a two function defined as f(x)=|x|+x and g(x)=|x|-x...

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  9. 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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  10. 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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  11. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equal...

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  12. Let f: RrarrR and g: RrarrR be two functions such that fog(x)=sin...

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

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

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

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

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  17. Show that f: R-[0]vecR0[0] given by f(x)=3/x is invertible and it is i...

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  18. Let A={1,2,..., n} and B={a , b }. Then number of surjections from A...

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  19. If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) e...

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  20. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

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