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TiliK225 [7]
3 years ago
10

If f(x) = log2 (x + 4), what is f−1(3)?

Mathematics
1 answer:
Kaylis [27]3 years ago
7 0
Now, to get the inverse "relation", we first, do a quick switcharoo on the variables, and then solve for "y".

\bf f(x)=y=log_{2}(x+4)\qquad inverse\implies \boxed{x}=log_{2}\left(\boxed{y}+4  \right)\\\\
-------------------------------\\\\
\textit{Logarithm Cancellation Rules}\\\\
log_{{  a}}{{  a}}^x\implies x\qquad \qquad 
{{  a}}^{log_{{  a}}x}=x\\
~~~\qquad \qquad \qquad \qquad \qquad \uparrow \\
~\qquad \qquad \qquad \textit{let's use this rule}\\\\
-------------------------------\\\\


\bf 2^x=2^{\cfrac{}{}log_{2}(y+4)}\implies 2^x=y+4\implies 2^x-4=y\impliedby f^{-1}
\\\\\\
thus\qquad 2^3-4=f^{-1}(3)\implies 8-4=f^{-1}(3)\implies 4=f^{-1}(3)
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Find a fraction equivalent to 5/7 whose squared terms add up to 1184.
bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y  } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}

                                                              \large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \  \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28  } \end{gathered}$}

                                                                  \large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20  } \end{gathered}$}

The fraction that satisfies the request is \bf{\dfrac{20}{28}} , since in \bf{\dfrac{-20}{-28}} the negative signs are canceled and the first fraction is obtained.

3 0
2 years ago
How to estimate 96 Times 34 what is the answer
Marrrta [24]

When it says to estimate, I always think of doing it by hand to show work.  So set it up like this:

  96

<u>x 34</u>

So follow it out multiplying across 4*6 and 4*9 carrying over as needed to get it to look like this:

  96

<u>x 34</u>

384


Do the same for the 3 to get this:

  96

<u>x 34</u>

  384

2880

Add 384+2880=3264

Your final answer is 3,264

6 0
3 years ago
June was thinking of a number. June doubles it, then adds 18 to get an answer of 90.7. What was the original number?
stiv31 [10]

Answer:

81.7

Step-by-step explanation:

90.7-18 divided by 2 = 81.7 or 82 simplified

8 0
3 years ago
Help please last one
Monica [59]
Y=1/2x+8


Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
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2 years ago
Will the opposite of a number always sometimes or never be greater than the number itself
stealth61 [152]
Sometimes, because if the number is negative, the opposite is greater, but if the number is positive, the opposite is smaller.
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