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If f(x)=(3x-2)/(2x-3), prove that f(f(x)...

If `f(x)=(3x-2)/(2x-3),` prove that `f(f(x)))=x` for all `x in R-{3/2}` .

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To prove that \( f(f(x)) = x \) for the function \( f(x) = \frac{3x - 2}{2x - 3} \), we will follow these steps: ### Step 1: Substitute \( f(x) \) into itself We start by substituting \( f(x) \) into itself: \[ f(f(x)) = f\left(\frac{3x - 2}{2x - 3}\right) \] ...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

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  2. If f(x) = x/(sqrt(1+x^2) then fofof(x)

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  3. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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

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  5. Let f: RvecR be a function given by f(x)=a x+b for all x in R . Fi...

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

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  7. 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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  8. 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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  9. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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

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

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  15. 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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  16. 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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  17. 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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  18. Let f: RrarrR and g: RrarrR be two functions such that fog(x)=sin...

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

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

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