Question

For f(x)=3x+1 and g(x)=(x^2)-6, find (f+g)(x).

Answer 1

Answer:
`(f+g)(x)=x^2+3x-5.`

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

`f(x)=3x+1,\\\\g(x)=x^2-6.`

We are to find the value of (f + g)(x).

We know that

for any two functions p(x) and q(x),

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

Therefore, we get

`(f+g)(x)\\\\=f(x)+g(x)\\\\=(3x+1)+(x^2-6)\\\\=3x+1+x^2-6\\\\=x^2+3x-5.`

Thus,
`(f+g)(x)=x^2+3x-5.`

Answer 2

`f(x)=3x+1;\ g(x)=x^2-6\\\\(f+g)(x)=(3x+1)+(x^266)=3x+1+x^2-6=x^2+3x+(1-6)\\\\=\boxed{x^2+3x-5}`