Maxima & Minima Explained Visually | First & Second Derivative Concept #maths #calculus

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

find domain and range | class 11 maths | functions class 11 #algebra #mathematics

Mathematics ( Functions ; Hyperbole ; Vertical and Horizontal asymptotes; Grade 10/11/12 ) #mathematics #grade10 #functions #hyperbole #asymptote

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

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

functions | relations-functions class11 revision notes #maths #function

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