Algebra II: f(x) & g(x)

Question

Let f(x)= 3x^5+5x. Evaluate the function f(-x). What conclusion can be made?

a. the function is both an even and an odd function

b. the function is an odd function

c. the function is neither an even nor an odd function

d. the function is an even function

Answer 1

Heaven, the website Mathwords disagrees with Michael.

According to Mathwords, a function is odd if and only if f(–x) = –f(x).

Michael says this would be an even function.

As Sam says, the answer is (b)

Answer 2

Let f(x)= 3x^5+5x. Evaluate the function f(-x). What conclusion can be made?

a. the function is both an even and an odd function

b. the function is an odd function

c. the function is neither an even nor an odd function

d. the function is an even function

To evaluate the function of -x, we plug -x into the function everywhere we see x. The easiest way to do this is to rewrite the equation with a parenthesis substituted for every x.

3( )⁵ + 5( )

then insert the -x into the empty parenthesis

3(-x)⁵ + 5 (-x)

next get rid of the parenthesis by preforming the indicated operations, and compare the result of f(-x) to f(x)

By definition

if f(x) = f(-x) then it is an odd function

if f(x) = -f(-x) then it is an even function

and if neither of the above is true, than it is neither an odd nor an even function.

Answer 3

Because the powers are odd; it remains odd. (b)