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Let a function f:R^(+) to R is defined a...

Let a function `f:R^(+) to R` is defined as `f(x)="log"_(e)x,` then find each of the following:
(i) Range of `f`
(ii) `{:f(x)=-2}`
(iii) Is `f(xy)=f(x)+f(y)` true ?

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The correct Answer is:
(i) R `" "` (ii) `e^(-2) " "` (iii) Yes
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS-Exercise 2C
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  2. If a function f:R to R is defined as f(x)=x^(2)+1, then find each of t...

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  3. Let a function f:R^(+) to R is defined as f(x)="log"(e)x, then find ea...

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  4. A function F(c) is defined as : F(c) =(9)/(5)*c+32. Evaluate each ...

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  5. If f(x)=2x-5 , then evaluate the following: (i) f(0) (ii) f(7) (...

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  6. If f(x)=x^(2), then evaluate: (f(1*2)-f(1))/(1*2-1)

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  7. If f(x)=x^(2) , then evaluate : (f(x+1)-f(x-1))/(4x)

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  8. If f(x)=(x)/(x-1), then evaluate : (f(a//b))/(f(b//a))

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  9. If f(x)=(x-1)/(x+1), then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a...

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  10. If f(x)=(1)/(1-x), then prove that : f[f{f(x)}]=x

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  11. If (x)=tan x, the prove that :f(x)+f(-x)=0

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  12. If f(x)=x+(1)/(x), then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x)...

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

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  14. If y(x)=sin x + cos^(2)x, then prove that: f(x)=f(pi-x)

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  15. If f(x)=(1-x^(2))/(1+x^(2)), then prove that: f(tan theta)=cos 2thet...

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  16. If f(x)=x^2+x+1, then find the value of 'x' for which f(x-1) =f(x)

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  17. If f(x)=log(e)x, then prove that :f(xyz)=f(x)+f(y)+f(z)

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  18. If f(x)=log(e)x and g(x)=e^(x), then prove that : f(g(x)}=g{f(x)}

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  19. If f(x)=sqrt((1-x)/(1+x)), then evalaute :f(cos 2theta)

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  20. If f(x)="log"(1+x)/(1-x) , then prove that: f((2x)/(1+x^(2)))=2f(x)

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