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3 years ago

Determine algebraically whether the function g(x)=x^2 is even odd or neither

Mathematics

2 answers:

irina1246 [14]3 years ago

8 0

g(x) = x^2

g(-x) = (-x)^2 ... replace every x with -x

g(-x) = x^2 ... squaring a negative makes it positive

So because g(x) = g(-x) for every x, this means g(x) is an even function. For polynomials, if every exponent is even, then the entire polynomial is even as well.

Note: if a function is even, then it won't be odd or vice versa unless the function is the zero function. In other words, g(x) = 0 is both even and odd.

julsineya [31]3 years ago

5 0

I think its 2 because its 2 so you will put 2

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3 years ago

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Katyanochek1 [597]

Answer:

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3 years ago

Math question. Please help

yanalaym [24]

To find the perimeter of the triangle, you need to know the length of the hypotenuse (h). Use the Pythagorean theorem to find it.
.. h^2 = (4w)^2 + (15/2*w)^2
.. = w^2*(4^2 +(15/2)^2)
.. = w^2*(16 +56 1/4)
.. = w^2*(72 1/4)
Taking the square root, we find the hypotenuse to be
.. h = √(w^2*72.25) = 8.5w = (17/2)w

Now, the length of the triangle's perimeter is the sum of the lengths of the sides.
.. P = 4w +(15/2)w +(17/2)w
.. P = 20w

The area of the triangle is half the product of base and height:
.. A = (1/2)(4w)(15/2*w)
.. A = 15w^2

So, the ratio of perimeter to area is
.. P/A = (20w)/(15w^2) = 4/(3w) . . . . . . . . simplified expression for P/A

The problem is asking you to find (and graph) the values of w such that
.. P/A < 1
.. 4/(3w) < 1 . . . . . . substitute our value of P/A
.. 4/3 < w . . . . . . . . multiply by w

This is graphed with an open circle around the point 1 1/3, and a solid arrow to the right of that circle. The open circle shows that w=4/3 is NOT a solution, but all values greater than that are.

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3 years ago