Does it imply make $x$ the topic?
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Great inquiry. This is an expression carapeastra.netematicians and also carapeastra.netematics educators utilize a whole lot, as well as it has a particular implying that isn"t completely clear to the student.

Idiomatically talking, to create a feature "in regards to" a provided variable or variables implies to create an algebraic expression making use of just that variable or variables.

So for example, provided a formula $x +2 y-3z = 0$, we can resolve for $z$ in regards to $x$ and also $y$ as $z=\ frac 1 (x +2 y)$.

Essentially talking, terms are the items that make up an expression. So in the expression $8x ^ 2-8x$, $8x ^ 2$ as well as $8x$ are terms incorporated by the reduction feature. The expression is in regards to $x$ because each term in the expression has just the variable $x$ (as well as constants) in it.


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When it implies

share in regards to $x$

It indicates to reveal the amount you"re searching for in regards to $x$, the variable.

Consequently,

Considering that:

$$f(x) = 2x ^ 2 + 4x$$

So,

$$f(-2 x) = 2(-2 x)^ 2 + 4(-2 x) = 8x ^ 2 - 8x$$


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It implies discover the feature $g(x) = f(-2 x)$ as if everyobody that recognizes carapeastra.net can merely connect in any type of worth of $x$ to locate $g(x)$.

As an example, if $f(x) = \ transgression(x)$, then $f(-2 x) = \ wrong(-2 x)$, and even far better (constantly streamline if that is feasible!) $\ wrong(-2 x)=-\ transgression(2x)$ is the expression you are trying to find.


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To examine $f(-2 x)$, you will certainly initially calculate $x"=-2 x$, then $2x"^ 2 +4 x"$.

You are asked to get rid of the intermediate replacement action as well as think of a straight expression $g(x)=f(-2 x)$.

Clearly, $g(x)=f(-2 x)=2(-2 x)^ 2 +4(-2 x)=8x ^ 2-8x$, which is the response.


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