Question

f(x) = square root 3x+7 , g(x) = square root 3x-7

Find (f + g)(x).

Answer 1

Your basically building a new equation with the two functions given to you.
(sqrt(3x + 7)) + (sqrt(3x - 7)) = 0

Then just open up the brackets and simplify further.
sqrt(3x + 7) + sqrt(3x - 7)= 0

Nothing to special really happened there, just removed the brackets. Now you move one of the radicals to the other side so you can square the whole equation.
sqrt(3x + 7) = - sqrt(3x - 7)

Then go ahead and square both sides to remove the radical.
3x + 7 = 3x - 7

Now if you kept trying to isolate x, you find that both sides will just cancel each other out and you are left with,
7 = -7

Since that statement isn't true your answer will be that there is no solution to this equation.
x ∈ Ø

Answer 2

Answer:

The solution is $(f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}$

Step-by-step explanation:

We need to find out the $(f+g)(x)$

Given functions are :

$f(x)=\sqrt{3x+7}$             ........(1)

and $g(x)=\sqrt{3x-7}$     ........(2)

To find out the $(f+g)(x)$, we need to add f(x) and g(x)

From equation (1) and (2)

$(f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}$

Therefore, the solution is $(f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}$