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Let f: x → x be an inveertable function. show that f has unique inverse
|
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1
|
577
|
April 10, 2019
|
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Consider f : R+ → [-5,∞] given by f(x) = 9x2 + 6x - 5
|
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1
|
1339
|
April 10, 2019
|
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Consider f : R+ → [4, ∞] given by f(x) = x2 + 4.show that f is invertible with the inverse
|
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1
|
3405
|
April 10, 2019
|
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Show that f : [-1,1] → R is given by f(x) = x/(x+2) is one-one
|
|
1
|
609
|
April 10, 2019
|
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State with reason whether following functions have inverse:
|
|
1
|
494
|
April 10, 2019
|
|
Find gof and fog, if (i) f(x) = |x| and g(x) = 15x - 21
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1
|
1049
|
April 10, 2019
|
|
Let f, g and h be functions from R to R. Show that: (f + g) oh = foh + goh
|
|
1
|
562
|
April 10, 2019
|
|
Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by
|
|
1
|
393
|
April 10, 2019
|
|
Let f : R → R be defined as f(x) = 3x Choose the correct answer:
|
|
1
|
783
|
April 10, 2019
|
|
Let f : R → R be defined as f(x) = x4. Choose the correct answer: (A) f is one-one onto
|
|
1
|
672
|
April 10, 2019
|
|
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by B defined by
|
|
1
|
981
|
April 10, 2019
|
|
Let f : N → N be defined by f(n) = { n+1/2, if n is odd n/2, if n ids odd
|
|
1
|
1027
|
April 10, 2019
|
|
Let A and B be sets. Show that f : A x B → B x A such that f(a,b) = (b,a) is bijective function
|
|
1
|
677
|
April 10, 2019
|
|
In each of the following cases, state whether the function is one-one,
|
|
1
|
418
|
April 10, 2019
|
|
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f(x) = {(1, 4), (2, 5), (3, 6)} be a function from A to B
|
|
1
|
251
|
April 10, 2019
|
|
Show that the Signum Function f : R → R, given by f(x) = { 1, if x>0
|
|
1
|
855
|
April 10, 2019
|
|
Show that the Modulus Function f : R → R , given by f(x) = |x|, is neither one-one nor onto,
|
|
1
|
836
|
April 10, 2019
|
|
Prove that the Greatest integer Function f : R → R, Prove that the Greatest integer Function f : R → R,
|
|
1
|
453
|
April 10, 2019
|
|
Check the injectivity and surjectivity of the following functions:
|
|
1
|
961
|
April 10, 2019
|
|
Show that the function f: R* → R* defined by f(x) = 1/x is one - one and onto, where R*
|
|
1
|
460
|
April 10, 2019
|
|
Let R be the relation in the set N given by R = {(a,b) : a = b - 2,b > 6} Choose the correct answer:
|
|
1
|
524
|
April 10, 2019
|
|
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3),
|
|
1
|
321
|
April 10, 2019
|
|
Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2)
|
|
1
|
796
|
April 10, 2019
|
|
Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2
|
|
1
|
562
|
April 10, 2019
|
|
Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2},
|
|
1
|
726
|
April 10, 2019
|
|
Show that the relation R in the set A of points in a plane given by R = {(P. Q) : distance of the point P
|
|
1
|
469
|
April 10, 2019
|
|
Give an example of a relation, which is: (i) Symmetric but neither reflexive nor transitive
|
|
1
|
1508
|
April 10, 2019
|
|
Show that each of the relation R in the set A = { x ∈ Z : 0 ≤ X ≤ 12}, given by:
|
|
1
|
535
|
April 10, 2019
|
|
Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a,b) : |a - b| is even}
|
|
1
|
310
|
April 10, 2019
|
|
Show that the relation R in the set A of all the books in a library of a college,
|
|
1
|
464
|
April 10, 2019
|