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If RR is the set of real numbers and f(x...

If `RR` is the set of real numbers and `f(x)=|x|,g(x)=x`, find the product function fg.

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The correct Answer is:
`(fg)(x)={:{(x^2" when "x ge0),(-x^2" when "x lt0):}`
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CHHAYA PUBLICATION-RELATION AND MAPPING -Very short answer type questions
  1. If f(x)=5^x , then prove : f(x+y)=f(x).f(y)

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  2. If f(x)=5^x , then prove : (f(x+1))/(f(x-1))=25

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  3. If f(x)=5^x , then prove : f(log5x)=x

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  4. If f(x)=a.(x-b)/(a-b)+b.(x-a)/(b-a), show that, " "f(a)+f(b)=f(a...

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  5. If phi(x)=logex, then show: phi(e^x)=x

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  6. If phi(x)=logex, then show: phi(x^m)= mphi(x)

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  7. If phi(x)=logex, then show: phi(xy)=phi(x)+phi(y)

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  8. If phi(x)=logex, then show: phi(x/y)=phi(x)-phi(y)

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  9. If f(x)=e^(px+q) [p and q are constants], show that, f(a).f(b).f(c)=...

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  10. If f(x)=|x|-2x , find f(-1),f(1) and f(-h).

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  11. If g(x)=(x-a)/(x)+(x)/(x-b) , prove that, g((a+b)/(2))=(4ab)/(a^2-b^2)

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  12. If f(x)=(1)/(x^2) , show that f(x+h)-f(x-h)=-(4xh)/((x^2-h^2)^2).

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  13. If g(theta)=(1-tantheta)/(1+tan theta) , find the value of g(pi/4-thet...

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  14. If f(x)=loge.(1+x)/(1-x) , show that f((2x)/(1+x^2))=2f(x).

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  15. If f(x)=logex and g(x)=e^x, prove that f{g(x)}=g{f(x)}.

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  16. If f(x)=10x^2 - 13x+13 solve the equation f(x) = 16.

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  17. If f(x)=4[x]-3|x|, find f(3.5) and f(-3.5).

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  18. If RR is the set of real numbers and f(x)=|x|,g(x)=x, find the product...

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  19. Find the value of [-3]+[-3.6]-|2.6|+|-3|.

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  20. If f (x) =(x-1)/(x+1), then the value of f (2x) in terms of f(x) is-

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