Q) Show that the function 𝑓:𝑅→𝑅 defined by 𝑓(𝑥)=4𝑥^3−5,∀𝑥∈𝑅 is one-one and onto

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Q) Consider the quadratic equation (n^2−2n+2) x^2−3x+(n^2−2n+2)^2=0, n∈R. Let 𝛼 be the minimum

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

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