The function is given as,
[tex]\begin{gathered} f(x)=3x^2-7x+5 \\ g(x)=x^2+16 \end{gathered}[/tex]
( a )
[tex](f+g)(x)\text{ = f\lparen x\rparen + g\lparen x\rparen}[/tex]
Substituting the value of function we get,
[tex]\begin{gathered} (f+g)(x)\text{ = 3x}^2-7x+5+x^2+16 \\ (f+g)(x)\text{ = 4x}^2-7x+21 \end{gathered}[/tex]
Thus the value of the f(x+g)(x) is,
[tex](f+g)(x)=4x^2-7x+21[/tex]
(b) The required value is,
[tex](f-g)(x)\text{ = f\lparen x\rparen-g\lparen x\rparen}[/tex]
Substituting the value of function,
[tex]\begin{gathered} (f-g)(x)\text{ = \lparen3x}^2-7x+5)-(x^2+16) \\ (f-g)(x)\text{ = 3x}^2-7x+5-x^2-16 \\ (f-g)(x)\text{ = 2x}^2-7x-11 \\ \end{gathered}[/tex]
Thus the value of (f-g)(x) is,
[tex](f-g)(x)\text{ = 2x}^2-7x-11[/tex]
(c) The required value is,
[tex](f.g)(x)[/tex]
Substituting the value of function,
[tex]undefined[/tex]
