Given the function f(x)=-(1)/(6)-4x^(2), then what is f(3x) as a simplified polynomial? Answer:

Understand Function: Understand the function and what is being asked. We are given the function f(x) = -(1/6) - 4x^2 and we need to find f(3x), which means we need to substitute 3x for every x in the function f(x).Substitute 3x: Substitute 3x into the function. f(3x) = -(1/6) - 4(3x)^2 Now we need to simplify the expression.Simplify Squared Term: Simplify the squared term. (3x)^2 = 9x^2 Now we substitute this back into the expression. f(3x) = -(1/6) - 4 * 9x^2Multiply Constants: Multiply the constants with the squared term. 4 * 9x^2 = 36x^2 Now we substitute this back into the expression. f(3x) = -(1/6) - 36x^2Combine Terms: Combine the terms to get the final simplified polynomial. f(3x) = -36x^2 - (1/6) This is the simplified polynomial for f(3x).

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Given the function
f(x)=-(1)/(6)-4x^(2), then what is
f(3x) as a simplified polynomial?
Answer:

Given the function $f(x)=-\frac{1}{6}-4 x^{2}$ , 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

Full solution

Q. Given the function

f(x)=-\frac{1}{6}-4 x^{2}

, then what is

f(3 x)

as a simplified polynomial?

\newline

Answer:

Understand Function: Understand the function and what is being asked. $\newline$ We are given the function $f(x) = -(\frac{1}{6}) - 4x^2$ and we need to find $f(3x)$ , which means we need to substitute $3x$ for every $x$ in the function $f(x)$ .
Substitute $3x$ : Substitute $3x$ into the function. $\newline$ $f(3x) = -(\frac{1}{6}) - 4(3x)^2$ $\newline$ Now we need to simplify the expression.
Simplify Squared Term: Simplify the squared term. $\newline$ $(3x)^2 = 9x^2$ $\newline$ Now we substitute this back into the expression. $\newline$ $f(3x) = -(\frac{1}{6}) - 4 \times 9x^2$
Multiply Constants: Multiply the constants with the squared term. $\newline$ $4 \times 9x^2 = 36x^2$ $\newline$ Now we substitute this back into the expression. $\newline$ $f(3x) = -(\frac{1}{6}) - 36x^2$
Combine Terms: Combine the terms to get the final simplified polynomial. $\newline$ $f(3x) = -36x^2 - \frac{1}{6}$ $\newline$ This is the simplified polynomial for $f(3x)$ .