Please help me with the following 5 questions. Thanks in advance.
31. (a) If A={1,2,3,4} and B={-1,3}, then what is the number of onto functions from A to B?
(b)If A={-1,2,3} and B= {0,3,5} then what is the number of bijections from A to B?
(c)If A= {-1,2,3} and B= {0,3,5,7} then what is the number of bijections from A to B?
32. If f: R→R defined by f(x)= 7x2 + 13, find g: R→R such that fog= IR =gof
33. Prove that a function f : N→Z defined by f(n) = n-1/2 if n is odd and -n/2 if n is even
, is bijective. Find its inverse.
34. Show that f:Z→Z defined by f(x)=x2
+x is many-one and into ( neither 1-1 nor onto)
but f: R→R defined by f(x)=x3
+x is a bijection.
35. Let f, g: R→R be two functions. Consider the product function f×g: R→R.
With the help of an example show that
(a) if both f and g are onto, f×g need not be onto.
(b) if both f and g are one-one, f×g need not be one-one.
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Step-by-step explanation:
bijection functions means one one
many to one means 2 or more in image a to b
one one means relating 1 image to only one image
onto means from. b to a
into means the left over one
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