Question

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

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.