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Maths
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![maths - Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X"-1 f(x) = Ixll "(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X"-1 f(x) = Ixll "(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_709570_8f2868b_1778804704986_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=986_sc.jpg "maths - Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X\"-1 f(x) = Ixll \"(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X\"-1 f(x) = Ixll \"(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X - ShareChat")