Question

If f(x) = x^3+x-3 and g(x)= x^2 + 2x, then what is (f + g)(x)?

Answer 1

`(f + g)(x) = x^3 +x^2 +3x - 3`

Explanation:

Given

`f(x) = x^3+x-3`

`g(x)= x^2 + 2x`

Required

`(f + g)(x)`

`(f + g)(x)` is calculated as thus

`(f + g)(x) = f(x) + g(x)`

By substituting respective values of f(x) and g(x) in the above equation

`(f + g)(x) = f(x) + g(x)` becomes

`(f + g)(x) = x^3+x-3 +x^2 + 2x`

Collect like terms

`(f + g)(x) = x^3 +x^2 +x + 2x - 3`

Perform arithmetic operations on like terms

`(f + g)(x) = x^3 +x^2 +3x - 3`

The expression cannot be simplified any further;

Hence,
`(f + g)(x) = x^3 +x^2 +3x - 3`