Given the following statements: I. The function f(x) = x^{2}

sunshine022uv

sunshine022uv

Answered question

2021-12-26

Given the following statements:
I. The function f(x)=x2sin2x is an odd function.
II. The function f(x)=exsinx is a neither function.
III. The function f(x)=cos(5x)sin2x is an even function
IV. The function f(x)=(x5)e2x is an even function.

Answer & Explanation

puhnut1m

puhnut1m

Beginner2021-12-27Added 33 answers

Step 1
we know that: put x=x and then,
f(x)=f(x) even function
f(x)=f(x) odd function
f(x)f(x)orf(x) neither function
Step 2
I) The function f(x)x2sin2x is odd function
So,
put x=x in function:
f(x)=(x)2(sin(x))2
=x2(sin)2
f(x)=x2(sin)2
So, f(x)f(x) [this is a even function not odd function] (statement false)
amarantha41

amarantha41

Beginner2021-12-28Added 38 answers

II) The function f(x)=exsinx is a neither function:
put x=x
f(x)=e(x)sin(x)=ex(sinx)
f(x)=exsinx
f(x)K or f(x)
So, This is a neither function (statement true)
karton

karton

Expert2022-01-09Added 613 answers

III)
Step 3
The function f(x)=Gx(5x)sin2x is even function
So, put x=x
f(x)=Gx(5(x))(sin(x))2
=Gx(5x)(sinx)2
f(x)=Gx(5x)sin2x
=f(x)
So, This is a even function
IV) The function f(x)=(x5)e2x is an even function.
put x=-x
So,
f(x)=(x5)(e)2(x)
=(x+5)e2x
-f(x) or p(x)

So, This is a neither function

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?