Question

If f(x) = 3x^2 - 2 and g(x) = 4x + 2

what is the value of (f + g)(2) ?

please show work!!

Answer 1

Hello!

The answer is:

`(f+g)(2)=20`

Why?

To solve the problem, we need to add the given functions, and then, evaluate the resultant function with the given value of "x" which is equal to 2.

We need to remember that:

`(f+-g)(x)=f(x)+-g(x)`

So, we are given the functions:

`f(x)=3x^2-2\\g(x)=4x+2\\`

Then, adding the functions , we have:

`(f+g)(x)=f(x)+g(x)=(3x^2-2)+(4x+2)`

`(f+g)(x)=3x^2-2+4x+2=3x^2+4x-2+2=3x^2+4x`

Therefore, we have that:

`(f+g)(x)=3x^2+4x`

Now, evaluating the function, we have:

`(f+g)(2)=3(2)^2+4(2)=3*4+4*2=12+8=20`

Hence, we have that the answer is:

`(f+g)(2)=20`

Have a nice day!