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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > What is meant by odd and even function ?
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What is meant by odd and even function ?

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Odd function : f(x)= -f(-x) Even function : f(x)=f(-x)
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Odd function: in a function f(x) when you substitue (-x) for all 'X' and it gives an output as -f(x) Ex: In a function f(x) =x^3 if we substitute (-x) in place of x then f(-x) =(-x)^3= -x^3 which is nothing but -f(x) Even function: when we substitute (-x) in place of x output will be f(x) only. Ex:...
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Odd function: in a function f(x) when you substitue (-x) for all 'X' and it gives an output as -f(x) Ex: In a function f(x) =x^3 if we substitute (-x) in place of x then f(-x) =(-x)^3= -x^3 which is nothing but -f(x) Even function: when we substitute (-x) in place of x output will be f(x) only. Ex: f(x)=x^2 when we substitute (-x) in place of x:- f(-x)=(-x)^2= x^2= f(x). read less
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Algebraically, In a function f(x), if you substitute x with -x and end up with the same result, then f(x) is an even function. So, f(x) = f(-x). Implication of this fact is that if you draw a curve of f(x), it will be symmetric about the y axis. Similarly, if f(x)=-f(-x), then you have an odd function....
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Algebraically, In a function f(x), if you substitute x with -x and end up with the same result, then f(x) is an even function. So, f(x) = f(-x). Implication of this fact is that if you draw a curve of f(x), it will be symmetric about the y axis. Similarly, if f(x)=-f(-x), then you have an odd function. Such functions produce curves symmetric about the origin. read less
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If a function is symmetrical about Y-AXIS it is a even function. Otherwise odd. Mathematically if F(-x)=F(x) is a even function. if F(-x)=-F(x) is a odd function
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If f(-x)=-f(x) for all x belongs to domain of"f" then f is called as" odd function".Ex:sin(-x)=-sinx If f(-x)=f(x) for all x belongs to domain of "f" then f is called as "Even functin".Ex:cos(-x)=cosx.
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Having 12+ years of experience in online and offline teaching

Odd symmetric about origin and even symmetric about y-axis.
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Hi, In simple terms, an odd function has a value - f(x) when x is less than 0 where f(x) being the output value for X greater than 0. Even function has a value f(x) for values greater than 0 as well as values less than 0.
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Theoretically, a function f(x) can be termed as even if:- f(x)= f(-x) a function f(x) is termed as odd if:- f(x)= -f(-x) While graphically, if a function is symmetrical about X=0 that is Y-axis then the function is termed as Even function while if a function is symmetrical about Origin or in Opposite...
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Theoretically, a function f(x) can be termed as even if:- f(x)= f(-x) a function f(x) is termed as odd if:- f(x)= -f(-x) While graphically, if a function is symmetrical about X=0 that is Y-axis then the function is termed as Even function while if a function is symmetrical about Origin or in Opposite quadrants then the function is termed as Odd function. read less
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Which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition:...
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Which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = xn is an even function if n is an even integer, and it is an odd function if n is an odd integer. read less
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If even function f(x)= f (- x) then it is called even function E.g.:- f( x ) = x^4 + x^2 - 2. f( -x)= (- x)^4 + (-x)^2 - 2= x^4 + x^2- 2 = f(x) If in function f (x), x is replaced by -x then we get then we called Odd function. Eg: f ( x)= x^3+x f(-x)= (-x)^3+ (-x) = -( x^3+x) it odd function.
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Hey Akshay try this for a change The positive rational numbers may be arranged in the form of a simple series as follows ( 1 / 1 ), ( 2 / 1 ), ( 1 / 2 ) , ( 3 / 1 ), ( 2 / 2 ), ( 1 / 3 ) , ( 4 / 1 ) , ( 3 / 2 ), ( 2 / 3), ( 1 / 4 ), ... Show that ( p / q ) is the [ ( 1 / 2 ) ( p + q - 1 ) ( p + q - 2 ) + q ] th term of the series. I see you like solving problems on mathematics so give it an honest try on your own Also to those boasting about years of experience in mathematics, please stop boasting about yourself before the rest of the teachers. If you are good, you are good and I do not doubt that. We all are here to help and not boast and this space is for questions only and not boasting. Hope you all keep this in mind.
As is visible, this relates to the partitioning of numbers without repetition. Let p+q = t Let us see the partitioning of 't' for 1st term 't' = 2 = 1+1 2nd term 3= 2+1 = 1+2 And so...
Santosh
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