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.

Given:

The two functions are:

To find:

The correct statement about the function .

Solution:

We have,

Adding both functions, we get

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

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

The range of 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.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.