Given the function f(x)=-(1)/(6)x-x^(2), 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) = -(1/6)x - x^2. This means we will replace every instance of x in f(x) with -3x.Substitute -3x into function: Substitute -3x into the function. f(-3x) = -(1/6)(-3x) - (-3x)^2Simplify first term: Simplify the first term. f(-3x) = (1/6)(3x) - (-3x)^2 f(-3x) = (1/2)x - (-3x)^2Simplify second term: Simplify the second term. f(-3x) = (1/2)x - (9x^2)Combine terms for final polynomial: Combine the terms to get the final simplified polynomial. f(-3x) = -9x^2 + (1/2)x

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Given the function
f(x)=-(1)/(6)x-x^(2), then what is
f(-3x) as a simplified polynomial?
Answer:

Given the function $f(x)=-\frac{1}{6} x-x^{2}$ , 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}{6} x-x^{2}

, 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 $f(x) = -\frac{1}{6}x - x^2$ . This means we will replace every instance of $x$ in $f(x)$ with $-3x$ .
Substitute $-3x$ into function: Substitute $-3x$ into the function. $\newline$ $f(-3x) = -(\frac{1}{6})(-3x) - (-3x)^2$
Simplify first term: Simplify the first term. $\newline$ $f(-3x) = \frac{1}{6}(3x) - (-3x)^2$ $\newline$ $f(-3x) = \frac{1}{2}x - (-3x)^2$
Simplify second term: Simplify the second term. $f(-3x) = (\frac{1}{2})x - (9x^2)$
Combine terms for final polynomial: Combine the terms to get the final simplified polynomial. $f(-3x) = -9x^2 + (\frac{1}{2})x$