Question

Consider f(x) = 2x2 + 1 and g(x) = 3x − 6. Which statement about f + g is true?

A. It is a linear function.
B. It is a quadratic function.
C. The domain is x ≥ −3.
D. The range is all real numbers.

Answer 1

Given:

The two functions are:

`f(x)=2x^2+1`

`g(x)=3x-6`

To find:

The correct statement about the function
`f+g`.

Solution:

We have,

`f(x)=2x^2+1`

`g(x)=3x-6`

Adding both functions, we get

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

`f+g=2x^2+1+3x-6`

`f+g=2x^2+3x-5`

It is a quadratic function. So, option A is incorrect and option B is correct.

The domain of
`f+g` is all real numbers because it is defined for all real values of x. So, option C is incorrect.

The range of
`f+g` cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.

Therefore, the correct option is B.