Given:
The two functions are:
[tex]f(x)=2x^2+1[/tex]
[tex]g(x)=3x-6[/tex]
To find:
The correct statement about the function [tex]f+g[/tex].
Solution:
We have,
[tex]f(x)=2x^2+1[/tex]
[tex]g(x)=3x-6[/tex]
Adding both functions, we get
[tex]f+g=f(x)+g(x)[/tex]
[tex]f+g=2x^2+1+3x-6[/tex]
[tex]f+g=2x^2+3x-5[/tex]
It is a quadratic function. So, option A is incorrect and option B is correct.
The domain of [tex]f+g[/tex] is all real numbers because it is defined for all real values of x. So, option C is incorrect.
The range of [tex]f+g[/tex] 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.
