Question

Check all of the functions that are odd.

Answer 1

For a function to be odd f(-x)=-f(x).

1) putting x as -x

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

Thus, this is an odd function.

2) Following the same procedure,

f(-x)= -x^5+3x^3-2x =-f(x)

Thus, this is an odd function.

3) Again,

f(-x)= -4x-9 = -f(x)

This also is an odd function.

Hope this helps :)

Answer 2

Answer:

1) $f(x)=x^{3}-x^{2}$ is not an odd function

2)$f(x)=x^{5}-3x^{3}+2x$ is an odd function

3)$f(x)=4x+9$ is not an odd function

Step-by-step explanation:

The function is odd, which satisfies the condition f(-x) = - f(x)

first we check for $f(x)=x^{3}-x^{2}$

Replace x with - x,

$f(-x)=(-x)^{3}-(-x)^{2}$

$f(-x)=(-x)^{3}-(x)^{2}$

we can't write this in the form of f(-x) = - f(x)

so, this is not an odd function

check for $f(x)=x^{5}-3x^{3}+2x$

Replace x with - x,

$f(-x)=(-x)^{5}-3(-x)^{3}+2(-x)$

$f(-x)=-((x)^{5}-3(x)^{3}+2(x))$

$f(-x)=-f(x)$

so, this is an odd function

check for $f(x)=4x+9$

Replace x with - x,

$f(-x)=4(-x)+9$

$f(-x)=-4x+9$

we can't write this in the form of f(-x) = - f(x)

so, this is not an odd function