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

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

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CHHAYA PUBLICATION-RELATION AND MAPPING -Short Answer Type Question
  1. If f(x)=(a-x^n)^(1/n)," where "a gt0 and n is a positive integer, show...

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

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

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

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

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

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

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

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

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

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

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

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  13. 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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  14. If f(x)=x^2+ax+bandf(1)=1,f(2)=2, find the value of f(3).

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  15. If the function f:RR to RR is given by f(x) = x for all x inRR and the...

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  16. If two real functions f and g are defined respectively by f(x)=sqrt(x+...

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  17. Find the range of the function f(x)=3-|x-3|.

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  18. Find f circgcirch, if f(x)=(x)/(x+1),g(x)=x^(10) and h(x)=x+3.

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  19. If f(x)=(4^x)/(4^x+2), then show that f(x)+f(1-x) =1.

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  20. Given f(x)=cos (logx), find the value of f(x).f(y)-(1)/(2)[f(x/y)+f(...

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