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What is $(f * g)(x)$ ? $\newline$ $f(x) = x + 1$ $\newline$ $g(x) = x^2$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Power rule with rational exponents

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = x + 1

\newline

g(x) = x^2

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Multiply functions: To find the product of the functions $f$ and $g$ evaluated at $x$ , denoted as $(f * g)(x)$ , we need to multiply the two functions together. $\newline$ $f(x) = x + 1$ $\newline$ $g(x) = x^2$ $\newline$ $(f * g)(x) = f(x) * g(x)$
Substitute expressions: Now we substitute the expressions for $f(x)$ and $g(x)$ into the product. $(f * g)(x) = (x + 1) * (x^2)$
Distribute $x^2$ term: Next, we distribute the $x^2$ term across the terms in the parentheses. $(f * g)(x) = x^2 * x + x^2 * 1$
Combine like terms: We simplify the expression by combining like terms and performing the multiplication. $\newline$ $(f * g)(x) = x^3 + x^2$

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