Summary - Mathematics

“In mathematics
the art of proposing a question
must be held of higher value than solving it.”
– Georg Cantor




FUNCTION
1 Classification of function


01. Constant function 03. Polynomial function
f(x) = k, k is a constant. y = f(x) = a0 xn + a1 xn-1+...+ an, n is non negative It is d
integer, ai are real constants. Given a0 ≠ 0, n is
the degree of polynomial function f ( x) =

02. Identity function There are two polynomial functions, f ( x) = 1 + x n & f ( x) = 1 − x n Dom
1 1
The function y = f ( x) = x , ∀x ∈ R satisfying the relation: f ( x) ⋅ f   = f ( x) + f  when
x x
Here domain & Range both R where ‘n’ is a positive integer.




2 Exponential function 3 Logarit


f(x) = ax, a > 0, a ≠ 1. f(x) = loga
0<a<1
0<a<1 a>1
y
y y

1
1
x' 1
x' x x' x x
O O O


y' y'
y'
Domain =R, Range = ( 0, ∞ )
Domain =



Proprieties of Log. Functions

1
1. 4 log a (xy) = log a | x | + log a | y | , where a > 0,a ≠ 1 and xy > 0 2. log a x =
log x a
for a > 0



x x
3. log a   = log a | x | − log a | y | , where a > 0,a ≠ 1 and > 0
y y
4. ( )
log a x n = n log a | x


m y
5. log a n x m = log|a| | x |, where a > 0,a ≠ 1 and x > 0 6. x loga = yloga x wher

n