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3 years ago

G(x) = 2 log(x - 1) what is the inverse

Mathematics

1 answer:

guapka [62]3 years ago

3 0

Answer:

$g^{-1}(x)=1+10^{x/2}$

Step-by-step explanation:

Inverse Function

Let's call:

$y=2 log(x-1)$

Divide by 2:

$y/2=log(x-1)$

Assuming the base of the log is 10, apply exponential base 10:

$10^{y/2}=x-1$

Solving for x:

$x=1+10^{y/2}$

Swap variables:

$y=1+10^{x/2}$

Calling this function the inverse:

$\boxed{g^{-1}(x)=1+10^{x/2}}$

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3Select the correct answerHow many solutions for x does the following equation have?2(x + 4) - 1 = 2x + 7OA. 7B.c.infiniteOD.1Re

Paladinen [302]

the initial equation is:

$4(8-x)=8$

So we can solve the equation to find the possible solution of the equation so:

$\begin{gathered} 8-x=\frac{8}{4}=2 \\ 8-2=x \\ 6=x \end{gathered}$

So the only possible solution of the equation is 6, so solution is option C

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1 year ago

Determine the minimum number of angle measures you would have to know to find the measures of all the angles formed by two paral

AlexFokin [52]

Answer:

Measure of one angle is required.

Step-by-step explanation:

Kindly refer to the image attached.

AM and BN are the two parallel lines cut by a transversal PQ.

The angles formed are:

$\angle 1, \angle 2, \angle 3, \angle 4, \angle 5, \angle 6, \angle 7 \ and\ \angle 8$ .

Let, only one of the angles is known to us.

Let, it is given that $\angle 2 = 60^\circ$

AM is a straight line, therefore

$\angle 1+\angle 2 =180^\circ\\\Rightarrow \angle 1 =180-60=120^\circ$

$\angle 1$ and $\angle 3$ are vertically opposite angles, therefore must be equal to each other.

$\angle 1 = \angle 3 = 120^\circ$

$\angle 2$ and $\angle 4$ are vertically opposite angles, therefore must be equal to each other.

$\angle 2 = \angle 4 = 60^\circ$

By Corresponding angle postulate, we can see the following:

$\angle 2=\angle 5 =60^\circ\\\angle 3=\angle 6 =120^\circ\\\angle 1=\angle 8 =120^\circ\\\angle 4=\angle 7 =60^\circ$

Therefore, by knowing just one angle, all the angles can be found.

6 0

3 years ago

If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?

Oduvanchick [21]

$\large\underline{\sf{Solution-}}$

Given:

$\rm \longmapsto x = a \sin \alpha \cos \beta$

$\rm \longmapsto y = b \sin \alpha \sin \beta$

$\rm \longmapsto z = c\cos \alpha$

Therefore:

$\rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta$

$\rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta$

$\rm \longmapsto \dfrac{z}{c} = \cos \alpha$

Now:

$\rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} }$

$\rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha$

$\rm = 1$

Therefore:

$\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1$

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3 years ago

Match the key aspect of a functions graph with its meaning.

jarptica [38.1K]

Answer:

1 - C

2 - A

3 - D

4 - B

Step-by-step explanation:

Consider an arbitrary function y=f(x).

1. f(x)>0 means y>0. y>0 determines all points on the graph which have positive y-coordinates. Positive y are corresponding to those x from the domain, for which graph lies above the x-axis. So 1 - C

2. f(x)<0 means y<0. y<0 determines all points on the graph which have negative y-coordinates. Negative y are corresponding to those x from the domain, for which graph lies below the x-axis. So 2 - A

3. To find y-intercept, we have to substitute x=0, so input is zero. Hence, 3 - D

4. To find x-intercept, we have to substitute y=0, so output is 0. Hence, 4 - B

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4 years ago

Read 2 more answers

Find sum of 100, 50, 25, 12.5

levacccp [35]

Add all the numbers together:

100+50= 150

150+25= 175

175+12.5= 187.5

187.5 is the sum.

I hope this helps!

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3 years ago

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