Question

The function :f R → R , defined by = xx)x(f , is an odd function. True or false​

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

The function :f R → R , defined by = xx)x(f , is an odd function. True or false

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

Given: f(−x)=−f(x)

f(x)+f(−x)=0. 

Hence, 

f(x)+f(−x)

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2

is a constant function.

Now, let g(x)=[∣f(x)∣+1]

⇒g(−x)=[∣f(−x)∣+1]=[∣f(x)∣+1]

 [Given: f(−x)=−f(x)], which is an even function.

Let P(x)= f(x)−f(−x)=f(x)/2 an odd function.

Answer 2

Answer:

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⭐Given⭐

➡f(−x)=−f(x)

➡f(x)+f(−x)=0.

✏Hence,

➡f(x)+f(−x)

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2 is a constant function.

Now, let g(x)=[∣f(x)∣+1]

⇒g(−x)=[∣f(−x)∣+1]=[∣f(x)∣+1]

[Given: f(−x)=−f(x)], which is an even function.

Let P(x)= f(x)−f(−x)=f(x)/2 an odd function.

Step-by-step explanation:

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