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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.

User Mkluwe
by
7.9k points

1 Answer

3 votes

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.

User Nassim Ben
by
8.5k points

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