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is a function which is- a.  one-one           b.  many-one         c. onto         d. into

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Give an example of a function which is one-one but not onto.

Give an example of a function which is one-one but not onto. which is not one-one but onto. (iii) which is neither one-one nor onto.

Following each of the following function find whether it is one-one or many-one and also into or onto f(x)=2tanx,(pi//2,3pi//2)toR

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Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into

If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, when x is rational and x, when x is irrational then (f-g) is A. one-one and onto B. neither one-one nor onto C. many one and onto D one-one and into

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto function then

Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into (3) one-one and onto (4) one- one and into

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The number of ordered pair (x ,\ y) satisfying correspondence C1 is 1 ...

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  2. The number of ordered pairs of integers (x,y) satisfying the equation ...

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  3. is a function which is- a.  one-one           b.  many-one         ...

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  4. p+r+2q= 1 b. 2 c. 0 d. 4

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  5. If bdot(log)(|"s"|)|p+q|=kdota then value of k is- 9/2 b. 6 c. (-3)/2 ...

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  6. Solve : cos ^(−1)(cos( (7π)/6) )

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  7. The number of integral values of k for which the equation sin ^−1 x+t...

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  8. If A ^2 −A+I=0 then A^(−1 ) =

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  9. The number of solution of the equation 2[x] = x + 1 + {x} is/are a. 1 ...

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  10. Solve : tan ^(−1) (tan((3π)/4))=

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  11. Solve: tan ^ (-1)tan((2pi)/3))

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  12. Draw the graph of the following function: f(x)=sin^(-1)(x+2)

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  13. Draw the graph of the following function: g(x)=cos^(-1)x

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  14. Draw the graph of the following function: h(x)=|tan^(-1)(3x)|\

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  15. If f(x) = cos^(-1)x + cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then :

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  16. If cos^(-1)x/a+cos^(-1)y/b=alpha , then (x^2)/(a^2)-(2x y)/(a b)cosalp...

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  17. Prove that : sin^(-1)3/5+sin^(-1)8/(17)=sin^(-1)(77)/(85)

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  18. cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

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  19. Prove: tan^(-1)2/3=1/2tan^(-1)(12)/5

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  20. If sin^2x + sin^2y < 1 ; x, y in R then prove that sin^-1(tanx . tany...

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