Question

Which statement is true about function f, which is shown in the graph? f(x) -8x⁵+ 4x³+5x?
A. Function f is neither even nor odd.
B. Function f is even.
C. Function f is odd.
D. function f is both even and odd.​

Answer 1

Answer:

f(-x)=-f(x)

So, Function f is odd

Option C is correct.

Step-by-step explanation:

Which statement is true about function f, which is shown in the graph?

f(x)= -8x⁵+ 4x³+5x?

Function is even if f(-x)= f(x)

and function is odd if f(-x)=-f(x)

Putting x=-x and finding f(-x)

f(-x)=-8(-x)^5+4(-x)^3+5(-x)

f(-x)=-8(-x^5)+4(-x^3)-5x

f(-x)=+8x^5-4x^3-5x

f(-x)=-(-8x^5+4x^3+5x)

f(-x)=-f(x)

So, Function f is odd

Option C is correct.

Answer 2

The function f(x) = -8x⁵+ 4x³+5x is an odd function option (C) Function f is odd is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -8x⁵+ 4x³+5x

Plug x → -x

f(-x) = -8(-x)⁵+ 4(-x)³+5(-x)

f(-x) = 8x⁵- 4x³-5x

f(-x) = -( -8x⁵+ 4x³+5x)

f(-x) = -f(x) (condition for odd function)

Thus, the function f(x) = -8x⁵+ 4x³+5x is an odd function option (C) Function f is odd is correct.

Learn more about the function here:

brainly.com/question/5245372

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