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A function f: R to R is defined as: f(...

A function `f: R to R` is defined as:
`f(x) ={{:(1,x in Q),(-1,x notinQ):}`
Evaluate each of the following:
(i) `f(2),f(pi)" "(ii)` Range of `f`
`(iii) f^(-1)(-1)" "(iv) f^(-1)(1)`

Text Solution

Verified by Experts

The correct Answer is:
(i) 1,-1 `" "` {1,-1} `" "` (iii) R - Q = set of irrational numbers
(iv) set of rational numbers
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS-Exercise 2C
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  2. Express each relation in the form of ordered pair and check whether is...

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  3. A function f: R to R is defined as: f(x) ={{:(1,x in Q),(-1,x notinQ...

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  4. Find which of the following are the function on set A={a,b,c} ? Give r...

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  5. A function f: R to R is defined asf(x)=x^(2)-1. Evaluate each of the f...

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  6. If A={-3,-2,-1,0,1,2,3} and f:A to Z is a function which of the follow...

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  7. If A={1,2,3,4},B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11...

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  8. If A={9,10,11,12,13} and a function f:A to N is defined as f(n)=larges...

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

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

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

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

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

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

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

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

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

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

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