Good question. This is a expression lutz-heilmann.infoematicians and also lutz-heilmann.info teachers use a lot, and it has actually a specific meaning that isn"t totally clear to the learner.
You are watching: What does in terms of x mean
Idiomatically speaking, to create a function “in terms of” a offered variable or variables means to write an algebraic expression making use of just that variable or variables.
So for instance, offered an equation $x+2y-3z = 0$, we deserve to fix for $z$ in terms of $x$ and also $y$ as $z=frac13(x+2y)$.
Literally speaking, terms are the pieces that create an expression. So in the expression $8x^2-8x$, $8x^2$ and also $8x$ are terms linked by the subtractivity feature. The expression is in terms of $x$ because each term in the expression has actually just the variable $x$ (and also constants) in it.
When it means
expush in terms of $x$
It means to expush the quantity you"re finding in regards to $x$, the variable.
$$f(x) = 2x^2 + 4x$$
$$f(-2x) = 2(-2x)^2 + 4(-2x) = 8x^2 - 8x$$
It indicates uncover the feature $g(x) = f(-2x)$ in such a way that everyobody that knows lutz-heilmann.info deserve to simply plug in any value of $x$ to discover $g(x)$.
For example, if $f(x) = sin(x)$, then $f(-2x) = sin(-2x)$, or even better (constantly simplify if that is possible!) $sin(-2x)=-sin(2x)$ is the expression you are trying to find.
To evaluate $f(-2x)$, you will initially compute $x"=-2x$, then $2x"^2+4x"$.
You are asked to rerelocate the intermediate substitution step and also come up through a straight expression $g(x)=f(-2x)$.
Obviously, $g(x)=f(-2x)=2(-2x)^2+4(-2x)=8x^2-8x$, which is the answer.
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