Why is this an odd function?

Question

f(x)=2x sqrt of (X^2 +3)

Answer 1

f ( x ) = ( 2 x ) √ ( x ² + 3 )
f ( - x ) = (- 2 x ) √ ( (- x) ² + 3 )
f ( - x ) = - ( 2 x ) √ ( x ² + 3 )
f ( x ) = - f ( x ) thus f ( x ) is an ODD function.

Answer 2

Ok...FIRST of all: The definition of an odd function is NOT f(-x) = -f(-x)

It is: f(-x) = -f(x)



The first factor (2x) is what gives you this result. Since the second has the x², that will be positive regardless of the sign of 'x'.

So, f(-x) = -2x

That and that alone is what gives you -f(x).

To illustrate this a little more clearly, let's let A = 2√(x² + 3)

Then you end up with f(x) = xA

Now take f(-x)_______you get: f(-x) = -xA.

Well...that is -f(x).

Do you see? That's all there is going on here. Nothing mysterious and the incorrect postings of odd/even functions is just going to confuse you.

Hope this helps.

Answer 3

definition of an odd function: - f(x) = f(-x)

let x = 1

x=2*(1) x sqrt(1²+3)
x=2 x sqrt(4)
x=2 x ±2
x=±4 therefore -f(x) = ±4

let x=-1

x=2*(-1) x sqrt(-1²+3)
x=-2 x sqrt(4)
x=-2 x ±2
x=±4 therefore f(-x) = ±4

therefore -f(x)=f(-x)

therefore odd function!!

Answer 4

because when you graph it, you will see that it revolves around the origin. which makes it an odd function.

but without graphing, if f(x) = -f(-x), then the function is odd.
lets use the number 1 for example.
f(1)= 2(1) sqrt (1^2 +3)
f(1) = 2 sqrt (4)
f(1) = 2 (2) = 4

now -f(-1) = -[2(-1) sqrt ((-1)^2 +3)]
-f(-1) = -(-2 sqrt 4)
-f(-1) = - (-2 (2)) = 4

f(x)=-f(-x) so it is odd.

Answer 5

f(x) = 2x * sqrt(x^2 + 3)

f(-x) = -2x * sqrt ((-x)^2 + 3) = -2x * sqrt(x^2 + 3)

Since -f(-x) = f(x), the function is odd.

Answer 6

For an odd function, f(-x)=-f(x) --- (1)
f(x)=2xsqrt(x^2+3)
f(-x)=2(-x)sqrt((-x)^2+3)=-2xsqrt(x^2+3)
-f(x)=-2xsqrt(x^2+3)
Identity (1) holds and so f(x) is an odd function.

Answer 7

for a function to be odd, f(-x)=-f(x)
you see.....
f(-x)= -2x sgrt(x^2 + 3)
-f(x)= -1* (2x sgrt (x^2 +3)=-2x sqrt (x^2+3)

Answer 8

because if u substitute the x with -x then f(x) = - f(-x)
f(-x) = -2x sqrt of (x^2 + 3) = - f(x)

Answer 9

An odd fuction is one in which f(-x) = -f(x). It has the property that it's symmetric about the origin. Just show that the given function follows that property and you're set.

On the side, an even function is one that follows f(-x) = f(x). It has the property that it's symmetric about the y-axis.

Answer 10

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