Given the function f(x)=-(1)/(3)x^(2)-(1)/(2)x, then what is f(-3x) as a simplified polynomial? Answer:

Understand function transformation: Understand the function transformation. We need to find f(-3x) using the given function f(x) = -(1/3)x^2 - (1/2)x. This means we will substitute -3x for every x in the function f(x).Substitute into function: Substitute -3x into the function. f(-3x) = -(1/3)(-3x)^2 - (1/2)(-3x)Simplify squared term: Simplify the squared term. f(-3x) = -(1/3)(9x^2) - (1/2)(-3x)Multiply by constants: Multiply the constants by the squared term. f(-3x) = -3x^2 - (1/2)(-3x)Simplify linear term: Simplify the linear term. f(-3x) = -3x^2 + (3/2)xCheck for simplification: Check for any possible simplification. The polynomial is already in its simplest form.

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Given the function
f(x)=-(1)/(3)x^(2)-(1)/(2)x, then what is
f(-3x) as a simplified polynomial?
Answer:

Given the function $f(x)=-\frac{1}{3} x^{2}-\frac{1}{2} x$ , then what is $f(-3 x)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Given the function

f(x)=-\frac{1}{3} x^{2}-\frac{1}{2} x

, then what is

f(-3 x)

as a simplified polynomial?

\newline

Answer:

Understand function transformation: Understand the function transformation. $\newline$ We need to find $f(-3x)$ using the given function $f(x) = -(\frac{1}{3})x^2 - (\frac{1}{2})x$ . This means we will substitute $-3x$ for every $x$ in the function $f(x)$ .
Substitute into function: Substitute $-3x$ into the function. $\newline$ $f(-3x) = -\left(\frac{1}{3}\right)(-3x)^2 - \left(\frac{1}{2}\right)(-3x)$
Simplify squared term: Simplify the squared term. $f(-3x) = -(\frac{1}{3})(9x^2) - (\frac{1}{2})(-3x)$
Multiply by constants: Multiply the constants by the squared term. $\newline$ $f(-3x) = -3x^2 - (\frac{1}{2})(-3x)$
Simplify linear term: Simplify the linear term. $f(-3x) = -3x^2 + \left(\frac{3}{2}\right)x$
Check for simplification: Check for any possible simplification. $\newline$ The polynomial is already in its simplest form.