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If y=f(x)=(ax-b)/(bx-a), prove that f(x)...

If `y=f(x)=(ax-b)/(bx-a),` prove that `f(x).f(1/x)` is independent of x.

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CHHAYA PUBLICATION-RELATION AND MAPPING -Short Answer Type Question
  1. If f(x)=(x-1)/(x+1), show that (f(a)-f(b))/(1+f(a)f(b))=(a-b)/(1+ab)

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  2. If f(x)=(1)/(1-x), show that, f[f{f(x)}]=x

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  3. If y=f(x)=(ax-b)/(bx-a), prove that f(x).f(1/x) is independent of x.

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  4. If y=f(x) =(px+q)/(rx-p), show that x = f(y).

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  5. If y=f(x)=(3x-5)/(2x-m)and f(y)=x, find the value of m.

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  6. If y=f(x)=(x-3)/(2x+1)and z=f(y), express z as a function of x.

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  7. If F(x)=(4x-5)/(3x-4), prove that F{F(x)} = x.

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  8. If f(x)=(a-x^n)^(1/n)," where "a gt0 and n is a positive integer, show...

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  9. If phi(x)=(1-x)/(1+x) prove that phi{phi(x)}=x

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  10. If phi(x)=(1-x)/(1+x) prove that phi{phi(cottheta)}=cottheta

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  11. If f(x)=tan^-1x, find the relation by which f(x),f(y) and f(x+y) are...

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  12. The function phi(x) is defined as follows: phi(x)=4, " when x is rat...

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  13. Let f(x)=2x^2-3," when "x le2 =2x+1," when "2ltxle3 =(1)/(2x-1)," ...

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  14. Find the values of x for which the following functions are undefined: ...

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  15. Find the values of x for which the following functions are undefined: ...

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  16. Find the values of x for which the following functions are undefined: ...

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  17. Find the values of x for which the following functions are undefined: ...

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  18. Find the values of x for which the following functions are undefined: ...

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  19. If the maximum and minimum value of f(x)=a+b sin x be 7 and 1 respecti...

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  20. If f(x)=ax^2+bx+c and f(x+1) =f(x)+x+1 is an identify, find the values...

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