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Answered

Given the functions, f(x) = x^3 + x^2 + 1 and g(x) = -6x^2 + 2, perform the indicated operations. When applicable, state the domain restriction.

(f + g)(x)

Verified Answer :

apologiabiology

easy
f(x)=x^3+x^2+1
g(x)=-6x^2+2
(f+g)(x)=
x^3+x^2+1-6x^2+2=
x^3+x^2-6x^2+1+2=
x^3-5x^2+3

(f+g)(x)=x^3-5x^2+3
domain is all real number

Answer:

Given functions,

\(f(x) = x^3 + x^2 + 1-----(1)\)

\(g(x) =-6x^2 + 2-----(2)\)

\((f+g)(x)=f(x)+g(x)\)

From equation (1) and (2),

\((f+g)(x)=x^3 + x^2 + 1-6x^2 + 2\)

Combine like terms,

\((f+g)(x)=x^3- 5x^2 + 3\)

Which is a polynomial.

∵ The domain of a polynomial is the set of all real numbers,

Hence, the domain of function (f+g)(x) is the set of all real numbers.

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