{"id":21903,"date":"2023-08-09T12:29:18","date_gmt":"2023-08-09T06:59:18","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=21903"},"modified":"2023-08-09T17:38:49","modified_gmt":"2023-08-09T12:08:49","slug":"inter-1st-year-maths-1a-functions-formulas","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/inter-1st-year-maths-1a-functions-formulas\/","title":{"rendered":"Inter 1st Year Maths 1A Functions Formulas"},"content":{"rendered":"

Use these Inter 1st Year Maths 1A Formulas<\/a> PDF Chapter 1 Functions to solve questions creatively.<\/p>\n

Intermediate\u00a01st Year Maths 1A Functions Formulas<\/h2>\n

Function:<\/strong>
\nLet A and B be non – empty sets and f be a relation from A to B. If for each element a e A, there exists a unique element b e B such that (a,b) \u2208 f, then f is called a function or mapping from A to B (or A into B). It is denoted by f: A \u2192 B. The set A is called the domain of f and B is called co-domain off.<\/p>\n

Illustration: Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25}. Consider the relation f(x) = x2<\/sup>, then f(1) = 1, f(2) = 4, f(3) = 9, f(4) = 16. Clearly each element in A has unique image in B. So, f: A \u2192 B.
\nf = {(1, 1) (2, 4) (3, 9) (4, 16)} is a function from A to. B.
\nClearly Domain (f) = {1,2, 3, 4} and Range (f) = {1, 4, 9, 16}
\nNote : The number of functions that can be defined from, a non-empty finite set A into a non-empty finite set B is [n(B)]n(A)<\/sup>.<\/p>\n

If f: A \u2192 B a function then f(A) = {f(a) \/ a \u2208 A} is called the range off. It is a subset of B (ie) f(A) \u2264 B.<\/p>\n

\"Inter<\/p>\n

One – one function (Injection):<\/strong>
\nLet f: A B, then f is said to be one-one function if different elements of A have different f- images in B. Thus f: A \u2192 B is one-one. (\u03bc) f: A B is an injection <=> ay a2 e A and f(a7) = f(aj implies that a1<\/sub> = a2<\/sub><\/p>\n

Illustration:
\nLetA = {1, 2, 3} and B = {2, 4, 6}. Consider f: A \u2192 B. f(x) = 2x then f(1) = 2, f(2) = 4 and f(3) = 6. Clearly f is a function from A to B such that different elements in A have different f – images in B.
\n\u2234 f: {(1, 2) (2, 4) (3, 6)} is one – one.<\/p>\n

Note : The number of one-one functions that can be defined from a non-empty finite set A into a non-empty finite set B is n(B) Pn(A)<\/sub> if n(B) \u2265 n(A) and zero if n(B) < n(A).<\/p>\n

Onto function (Surjection):<\/strong>
\nLet f: A \u2192 B. If every element of B occurs as the image of at least one element of in A, then fis an onto function. Thus f: A \u2192 B is surjection iff for each b e B, 3 a e A such that f(a) = b. Clearly fis onto \u21d4 Range (f) = B.<\/p>\n

Illustration; Let A = {-1, 7, 2, -2}, B = {1, 4} and Let f: A \u2192 B, be a function defined by f(x) = x2<\/sup>\u00a0then fis onto because f(A) = {f(-1), f(1), f(2), f(-2)} = {1, 4} = B.
\nNote : The number of onto functions that can be defined from a non – empty finite set A onto a two element set B is 2n(A)<\/sup> – 2 if n(A) \u2265 2 and zero if n(A) < 2.<\/p>\n

Bijective function :<\/strong>
\nA function f: A \u2192 B is a bijection if<\/p>\n