Find the arithmetic combination of f(x) =x+2, g(x)=x-2

The arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4,  (f g)(x) = ,

Solution:  

Given, two functions are f(x) = x + 2 and g(x) = x – 2

We need to find the arithmetic combinations of given two functions .

Arithmetic functions of f(x) and g(x) are (f + g)(x), (f – g)(x), (f g)(x),

Now, (f + g)(x) = f(x) + g(x)

= x + 2 +x – 2

= 2x

Therefore (f + g)(x) = 2x

similarly,

(f - g)(x) = f(x) - g(x)

= x + 2 –(x – 2)

= x + 2 –x + 2

= 4

Therefore (f - g)(x) = 4

similarly,

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

= (x + 2) (x – 2)

= x (x – 2) + 2 (x -2)

Therefore  (f g)(x) =

now,

=

Hence arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4,  (f g)(x) = ,

a is the right answer