Question

In each of the following cases state whether the function is bijective or not. Justify your answer.
(i) f: R → R defined by f (x) = 2x + 1
(ii) f: R → R defined by f(x) = 3 – 4x2

Answer 1

(i) f(x) = 2x + 1  

f(0) = 2(0) + 1 = 0 + 1 = 1  

f(1) = 2(1) + 1 = 2 + 1 = 3  

f(2) = 2(2) + 1 = 4 + 1 = 5

f(3) = 2(3) + 1 = 6 + 1 = 7

Different elements has different images  

∴ It is an one-one function.  

It is also an onto function.

The function is one-one and onto function.  

∴ It is a bijective function.

(ii) f(x) = 3 – 4x2

f(1) = 3 – 4(1)2  

= 3 – 4 = -1

f(2) = 3 – 4(2)2 = 3 – 16 = – 13  

f(3) = 3 – 4(3)2 = 3 – 36 = – 33  

f(4) = 3 – 4(4)2 = 3 – 64 = – 61  

It is not a bijective function. The positive numbers “R” do not have negative pre – image in X in R.

Answer 2

Answer:

sister plz refer above answer.........................................

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