Question

Which of the following is a true statement about functions

Answer 1

Explanation:

Its A.

Answer 2

The statement that is true about functions is:

If f and g are function then,

B. (f+g)(x)=f(x)+g(x)

Explanation:

A)

Let us define f(x)=x² and g(x)=1

then we have:

`(f(x))/(g(x))=x^2`

and

`(g(x))/(f(x))=(1)/(x^2)`

Hence, we get:

`(f(x))/(g(x))\\eq (g(x))/(f(x))`

Hence, option: A is incorrect.

B)

Option: B is always true.

(f+g)(x)=f(x)+g(x)

C)

Let us define f(x)=x²

Then

`f(a+b)=(a+b)^2=a^2+b^2+2ab`

and

`f(a)+f(b)=a^2+b^2`

Hence, we get:

`f(a+b)` is not always equal to
`f(a)+f(b)`

D)

Let us suppose
`f(x)=4x\ and\ g(x)=(1)/(x)`

Now,

`(fog)(1)=f(g(1))\\\\\\(fog)(1)=f(1)\\\\\\(fog)(1)=4`

and

`(gof)(1)=g(f(1))\\\\\\(gof)(1)=g(4)\\\\\\(gof)(1)=(1)/(4)`

Hence, we get:

`(fog)(x)` is not always equal to
`(gof)(x)`