Determine if the functions below are odd, even or neither.

(a) f(x) = x^2 + 2

(b) f(x) = (x^2 + 2)tan(x^2)

(c) f(x) = (x^2 + 2)sin (x)tan(x^2)

Solution Preview

To determine wether the function is even or odd, use the following rules:
For an even function, the following is true: f(x) = f(-x)
For an odd function, the following must be true: f(-x) = -f(x)

(a) f(x) = x^2 + 2 ...

Solution Summary

This solution illustrates and lists steps involved in determining if a function is odd, even or neither.

Which functions are one-to-one? Which functions are onto? Describe the inverse function
A)F:Z^2-N where f is f(x,y) x^2 +2y^2
B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd)
C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd)
D)h:N^3 -> N where h(x,y,z) = x + y -z

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c.)What is the inverse function of y=x^4
d.)What is the inverse function of (b.),y=x^2+4x?
e.)Is the inverse function from (d.), odd,even, or
neither?

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Please see the attached file for the fully formatted function.
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We have learned Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class and we have finished differentiation. We just started integration. In this problem we are not supposed to use any material we haven't learned, ie integration. We are using the books by Rudin, Ross, Morrey/Protter.
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Hello,
Can someone please help me with this home work problem? I am totally lost and stumped. I've read my text and notes several times and I don't get it. The problem is attached.
Thank you, in advance, for your help!