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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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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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Odd symmetric about origin and even symmetric about y-axis.
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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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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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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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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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