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If f(x)=(1)/(2)[3^(x)+3^(-x)], g(x)=(1)/...

If `f(x)=(1)/(2)[3^(x)+3^(-x)], g(x)=(1)/(2)[3^(x)-3^(-x)]` then `f(x)g(y)+f(y)g(x)=`

A

`f(x+y)`

B

`g(x+y)`

C

`2f(x)`

D

`2g(x)`

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. If f:Rrrarr RR and g: RR rarr RR are defined by f(x)=|x| and g(x)=[x-3...

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  2. If f(x) is defiend on [0, 1] as f(x)={{:(x","," if "x in Q),(1-x","," ...

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  3. If f(x)=(1)/(2)[3^(x)+3^(-x)], g(x)=(1)/(2)[3^(x)-3^(-x)] then f(x)g(y...

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  4. If f: A to B, g:B to C are two bijective functions then prove that gof...

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  5. If f:A to B is a bijective function then prove that (ii) f^(-1) of =...

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  6. To have inverse for the funciton f, f is

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  7. f:RrarrR is a function defined by f(x)=10x-7. If g=f^(-1) then g(x)=

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  8. If f:R rarrR is defined by f(x)=(2x+1)/(3) then f^(-1)(x)=

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  9. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , wher...

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  10. If f:R-{5//2}rarr R-{-1} defined by f(x)=(2x+3)/(5-2x) then f^(-1)(x)=

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  11. If f:R rarr R^(+) such that f(x)=(1//3)^(x), then f^(-1)(x)=

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  12. If f:[1, oo)rarr[2, oo) is given by f(x)=x+(1)/(x) then f^(-1)(x)=

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  13. If f:R^(+)rarrR such that f(x)=log(3)x then f^(-1)(x)=

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  14. If f:{1, 2, 3,……}rarr{0, pm1, pm2, …..} is defined by f(x)={{:(n//2,"...

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  15. The inverse of f(x)=(10^x-10^(-x))/(10^x+10^(-x))=

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  16. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

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  17. If f[1, oo)rarr[1, oo) is defined by f(x)=2^(x(x-1)) then f^(-1)(x)=

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  18. If f(x)=x-x^(2)+x^(3)-x^(4)+….oo when |x| lt 1 then f^(-1)(x)=

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  19. If f:R rarr R, g:R rarr R are defined by f(x)= 5x-3,g(x)=x^(2)+3, then...

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  20. If f:R rarr and g:R rarr R are defined by f(x)=3x-4 and g(x)=2+3x then...

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