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Express the following functions in the form of order pairs and find their range:
(i) `f:A to R, f(x)=x^(2)+5`, where `A={-2,-1,0,1}`
`g:A to N, g(x)=3x`, where `A:{x:x in N, x lt 4}`

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The correct Answer is:
(i) f = {(-2 , 9) , (-1,6) , (0,5) , (1,6) , (2,9)} , Range = { 5, 6,9}
(ii) g = { (1,3) , (2,6) , (3,9) , (4,12)} , Range = { 3,6,9 , 12}
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS-Exercise 2C
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  2. If A={1,2} and B={3,6} and two functions f: A to B and g: A to B are d...

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  3. Express the following functions in the form of order pairs and find th...

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  4. If a function f:R to R is defined as f(x)=x^(2)+1, then find each of t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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