Q) Let f:A→B be defined by f(x)=(x−2)/(x−3), where A=R−{3} and B=R−{1}. Discuss the biject

Q) Show that a function f: R → R defined by f(x) = 2𝑥/(1+𝑥^2 ) is neither one-one nor onto.

Q) Show that 𝑓:𝑅_+→[−5,∞) given by 𝑓(𝑥)=4𝑥^2+4𝑥−5 is both one-one and onto where 𝑅_+=[0,∞).

Q) Let A = R – {5} and B = R – {1}. Consider the function f: A → B, defined by f(x) = (𝑥−3)/

Q) Show that a function 𝑓:𝑅_+→𝐴⊂𝑁, defined as 𝑓(𝑥)=4𝑥^2+12𝑥+15 is one-one. Find gset 𝐴

Q) A function 𝑓:𝑅−{3/5}⟶𝑅−{3/5} is defined as 𝑓(𝑥)=(3𝑥+2)/(5𝑥−3). Show that 𝑓 is one-

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Q) Check whether the relation S in the set ℝ of real number, defined as S={(a,b):a≤b^2 } is reflexiv

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