Question

asked Oct 13, 2019 13.5k views

2 Answers

Cyclomarc · Answer 1 · 2019-10-19T22:06:19+0000

Answer:

The statement that is true about functions is:

If f and g are function then,

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

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)