Question

If f(x) = 3x + 7 and g(x) = 5x – 2 then (f+g)(x) = 8x + 5. True False

Answer 1

You are adding together functions f(x) and g(x) as follows:

f(x) + g(x) = 3x + 7 + 5x - 2. Combining like terms, 3x+5x=8x, and -2+5=3.

Thus, (f+g)(x) = 8x + 5. What is your conclusion?

Answer 2

Answer: The given statement is TRUE.

Step-by-step explanation: We are given the following two functions :

`f(x)=3x+7,~~~\textup{and}~~~g(x)=5x-2.`

We are to check whether the following statement is true or false :

`(f+g)(x)=8x+5.`

We know that for any two functions p(x) and q(x), we have

`(p+q)(x)=p(x)+q(x).`

Therefore, we get

`(f+g)(x)\\\\=f(x)+g(x)\\\\=(3x+7)+(5x-2)\\\\=3x+7+5x-2\\\\=8x+5.`

Thus,
`(f+g)(x)=8x+5.`

The given statement is TRUE.