Answer:
[tex](f + g)(x) = x^3 +x^2 +3x - 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^3+x-3[/tex]
[tex]g(x)= x^2 + 2x[/tex]
Required
[tex](f + g)(x)[/tex]
[tex](f + g)(x)[/tex] is calculated as thus
[tex](f + g)(x) = f(x) + g(x)[/tex]
By substituting respective values of f(x) and g(x) in the above equation
[tex](f + g)(x) = f(x) + g(x)[/tex] becomes
[tex](f + g)(x) = x^3+x-3 +x^2 + 2x[/tex]
Collect like terms
[tex](f + g)(x) = x^3 +x^2 +x + 2x - 3[/tex]
Perform arithmetic operations on like terms
[tex](f + g)(x) = x^3 +x^2 +3x - 3[/tex]
The expression cannot be simplified any further;
Hence, [tex](f + g)(x) = x^3 +x^2 +3x - 3[/tex]
