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If f(x)=e^(x) and g(x)=log(e)x, then sho...

If `f(x)=e^(x) and g(x)=log_(e)x,` then show that `"fog=gof"` and find `f^(-1) and g^(-1)`.

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SRISIRI PUBLICATION-FUNCTIONS-EXERCISE(VSAQ)
  1. If f(x)=(x-1)/(x+1),x ne pm1, show that fof^(-1)(x)=x.

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  2. If f:[1,oo) to [1,oo) is defined by f(x) = 2^(x(x-1)) then find f^(-1)...

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  3. If f(x)=e^(x) and g(x)=log(e)x, then show that "fog=gof" and find f^(-...

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  4. Let f(x) = x^(2), g(x) = 2^(x). Then solve the equation (fog)(x)=(gof)...

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  5. On what domain the functions f(x)=x^(2)-2x and g(x)=-x+6 are equal?

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  6. If f(x) = (cos^(2)x+sin^(4)x)/(sin^(2)x + cos^(4)x) AA x in R then sho...

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  7. If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(t...

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  8. Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,34,}. to B={1...

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  9. If the function f:{-1,1} to{0,2}, defined by f(x)=ax+b is a surjection...

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  10. If f:N to N is defined as f(x)=2x+5, is f onto?

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  11. Determine whether the functionf:R to (0,oo) defined by f(x) = 2^(x) ...

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  12. Determine whether the function f:(o,oo) to R defined by f(x) log(e)x i...

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  13. Determine whether the function f:R to [0,oo) defined by f(x)=x^(2) is ...

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  14. Determine whether the function f:R to [0,oo) defined by f(x)=x^(2) is ...

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  15. Determine whether the functionf:R to (0,oo) defined by f(x) = 2^(x) ...

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  16. If A={x:-1 le x le 1},f(x)=x^(2) and g(x)=x^(3), which of the followin...

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  17. If A={x:-1 le x le 1},f(x)=x^(2) and g(x)=x^(3), which of the followin...

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  18. Let A={1,2,3},B={a,b,c),C={p,q,r}. If f:A to B, g: B to C are defined ...

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  19. Determine whether the function f(x)=a^(x)-a^(-x)+sinx is even or odd.

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  20. Determine whether the function f(x)=sinx+cosx is even or odd.

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