Respuesta :
The value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
Explanation:
Given that the functions [tex]f(x)=4 x^{2}+1[/tex] and [tex]g(x)=x^{2}-5[/tex]
We need to determine the value of [tex](f+g)(x)[/tex]
The value of [tex](f+g)(x)[/tex] can be determined by substituting the value of [tex]f(x)[/tex] and [tex]g(x)[/tex] and simplifying the terms.
Thus, let us assign [tex]f(x)=4 x^{2}+1[/tex] in the function [tex](f+g)(x)[/tex], we have,
[tex]4 x^{2}+1+g(x)[/tex]
Now, let us assign [tex]g(x)=x^{2}-5[/tex] in the function [tex](f+g)(x)[/tex], we get,
[tex]4 x^{2}+1+x^{2}-5[/tex]
Grouping the like terms, we have,
[tex]4 x^{2}+x^{2}+1-5[/tex]
Adding the like terms, we get,
[tex]5 x^{2}-4[/tex]
Hence, the value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
