Can a function be both even and odd? use algebra to find the answer.

• if f(x) is an even number, then f(-x) = ? for all x.
• if f(x) is an odd number, then f(-x) = ? for all x.
• by the transitive property of equality, this means that f(x) = -f(x)
• combine like terms in the equation f(x) = -f(x)
= 0
divide both sides by 2.
f(x) =

• this function is both even and odd. in fact, it is the only function that is both even and odd. describe the function's graph, and state how it proves your conclusion.

fill in what the "? ? " are. you, much appreciated.

Im not sure exactly what you want the function to be. Because it can be any number. only the signs would change it

Step-by-step explanation:

okay so lets try this then..

if f(x) is an even number...let say 2

then f(-2)= 2x²+x+6

then it would be 2(-2²)+(-2)+6-4

https://www.symbolab.com/solver/step-by-step/F%5Cleft(x%5Cright)%3D-F%5Cleft(x%5Cright)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240