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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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The correct Answer is:
`e ^(x)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-FUNCTIONS -TEXTUAL EXERCISES (EXERCISE-1 (B)
  1. If f(x)=e^(x) and g(x)=log(e)x, then show that "fog=gof" and find f^(-...

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  2. If f(y)=(y)/(sqrt(1-y^(2))),g(y)=(y)/(sqrt(1+y^(2))) then show that ("...

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  3. If f: R to R and g: R to R are defined by f(x) = 2x^(2) +3 and g(x) = ...

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  4. If f : R to R, g : R to R are defined by f (x) = 2x ^(2) + 3 and g (x...

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  5. If f : R to R, g : R to R are defined by f (x) = 2x ^(2) + 3 and g (x...

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  6. If f : R to R, g : R to R are defined by f (x) = 2x ^(2) + 3 and g (x...

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  7. If f : R to R, g: R to R are defined by f (x) = 3x -1, g (x) = x ^(2) ...

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  8. If f:R to R , g:R to R are defined by f(x) = 3x-1, g(x)=x^(2)+1 then f...

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  9. If f : R to R, g: R to R are defined by f (x) = 3x -1, g (x) = x ^(2) ...

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  10. If f(x) = 1//x, g(x) = sqrt(x) for all x in (0,oo), then find (gof)(x)...

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  11. If f(x)=2x-1,g(x)=(x+1)/(2) for all x in R, find (gof)(x)

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  12. If f(x) = 2, g(x) = x^(2), h(x) = 2x then find (fogoh)(x)

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  13. Find the inverse of the following functions: If a, b in R, f : R to ...

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  14. f : R to (0, oo) defined by f (x) = 5 ^(x). then f ^-1(x)

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  15. f : R to (0, oo) defined by f (x) = log (2) (x). then f ^-1(x)

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  16. If f(x) = 1 + x + x^(2) + …… for |x| lt 1 then show that f^(-1)(x) = (...

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

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  18. If f(x)=(x-1)/(x+1),x ne pm1, show that fof^(-1)(x)=x.

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  19. If A={1,2,3},B=(alpha,beta,gamma),c=(p,q,r) and (f:A to B,g:B to C are...

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  20. If f: R to R, g : R to R defined by f(x) = 3x-2, g(x) = x^(2)+1, then ...

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