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oee [108]
3 years ago
6

What is the limit as x is approaching 0 of the absolute value of x

Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0
Recall that, an absolute value expression is a piece-wise in effect, thus we'd check the single-sided limits,

\bf \lim\limits_{x\to 0}~|x|\implies 
\begin{cases}
\lim\limits_{x\to 0^-}~-x\\\\
\lim\limits_{x\to 0^+}~+x
\end{cases}\implies 
\begin{cases}
0\\\\
0
\end{cases}\implies \lim\limits_{x\to 0}~|x|=0
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Answer:

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Step-by-step explanation:

So we have the equation:

y=5x+4

Let's write this in function notation. Thus:

y=f(x)=5x+4

A)

To flip a function over the x-axis, multiply the function by -1. Thus:

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Simplify:

-f(x)=-5x-4

B) To flip a function over the y-axis, change the variable x to -x. Thus:

f(x)=5x+4\\f(-x)=5(-x)+4

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To find the inverse, switch x and f(x) and solve for f(x):

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Switch:

x=5f^{-1}(x)+4

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Divide both sides by 5:

f^{-1}(x)=\frac{x-4}{5}

And we're done :)

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Step-by-step explanation:

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