Question

I need help determining whether the following functions are even, odd, or neither. Please help me.
1. f(x)=4x+5
2. f(x)=x^3-x-2
3. f(x)=x^4-x / x^5-x
4. f(x)= x^3-x / x^5

Answer 1

Remember that in order for a function to be even f(x)=f(-x) and in order to be odd you must make the whole function negative to be equal to f(-x)
The first one is neither , if you substitute the x by -x is not the same function as the one you presented in the beginning and is not odd because y I multiply the whole function by -1 it is not equal to f(-x).
2. Is neither

Answer 2

even: f(x)=f(-x)
odd: f(x)=-f(-x)

a) 4(3)+5 ? 4(-3)+5
17? [7 neither
b) (3)^2 -3-2 ? (-3)^3 -(-3)-2
4 ? 9 neither
c) (2^4-2)/( 2^5 -2) ? ((-2)^4-2)/((-2)^5 -(-2))
14/30 ? ( - 14/30) even
do the last on these same way...

Answer 3

If all the powers are odd, f(x) is odd. If all even, f(x) is even.

remember that constants are x^0, or even powers.