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Ludmilka [50]
3 years ago
15

Midpoint. (3,3), (-1,1)

Mathematics
1 answer:
Scilla [17]3 years ago
7 0

Answer:

1,2

Step-by-step explanation:

3+-1=2

2/2=1  

3+1=4

4/2=2

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If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
\\\\\\
inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
\\\\\\
\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\

\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
5 0
3 years ago
If p = 5 and q = 3 evaluate , 4p - pq
Fynjy0 [20]

Answer:

5

Step-by-step explanation:

4p-pq=4.5-3.5=20-15=5

7 0
3 years ago
Read 2 more answers
-X + 2y = 10<br> -3x+ 6y = 11
Tanzania [10]

Answer:

1. y = 1 /2X +5

Step-by-step explanation:

2. m=1/2

7 0
3 years ago
When does the graph of a quadratic function open upward of downward
sveticcg [70]
It opens upward when X is an even power. It would be for X squared or X raised to the 4th power.

6 0
3 years ago
If John drove 210 miles in 3 hours, how far will he have<br> driven in 4.5 hours?
VashaNatasha [74]

Answer:

3hours and 15 mins

Step-by-step explanation:

210 divied by 3=70

70=per hour

4 hours=280

70 divied by 2= 35

.5=35

280+35=315

315 miles in 4.5 hours

3 0
3 years ago
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