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miss Akunina [59]
3 years ago
9

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

Mathematics
2 answers:
JulijaS [17]3 years ago
8 0
f(x)=\log_2(x+4)\\
y=\log_2(x+4)\\
2^y=x+4\\
x=2^y-4\\
f^{-1}(x)=2^x-4\\\\
f^{-1}(3)=2^3-4=8-4=4
zalisa [80]3 years ago
3 0
f\left( x \right) =\log _{ 2 }{ \left( x+4 \right)  } \\ \\ \log _{ 2 }{ \left( x+4 \right)  } =y\\ \\ { 2 }^{ y }=x+4

\\ \\ x={ 2 }^{ y }-4\\ \\ \therefore \quad { f }^{ -1 }\left( x \right) ={ 2 }^{ x }-4\\ \\ \therefore \quad { f }^{ -1 }\left( 3 \right) ={ 2 }^{ 3 }-4=4
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In a restaurant, Chad tracked the number of children and adults that came in over an hour. During that time, 16 children and 40
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3 years ago
An element with mass 780 grams decays by 17.1% per minute. How much of the element is remaining after 19 minutes, to the nearest
VikaD [51]

Answer:

  22.1 grams

Step-by-step explanation:

At the end of each minute, (1 -17.1%) = 82.9% of the element remains. At the end of 19 minutes, the quantity has been multiplied by that value 19 times, so the remaining amount is ...

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3 0
2 years ago
The derivative of (x^2 +1)(x^3+ 1) (by definition and basic rule)
dlinn [17]

Answer:

f'(x) = 5x^4 + 2x + 3x^2

Step-by-step explanation:

To find the derivative of this equation we can do two things.

One method is to use the product rule, which states that when f(x) consists of two functions multiplied to each other (meaning f(x) = g(x) * h(x)), the derivative is f'(x) = g'(x)*h(x) + g(x)*h'(x). In simple language, the derivative is found by finding the derivative of x² + 1 and multiplying it with the normal function of x³ + 1, after which you add the product of the nnormal function of x² + 1 and the derivative of x³ + 1.

it might be clearer when I show you:

f(x) = (x^2 + 1)(x^3 + 1)\\f'(x) = (2x)(x^3 + 1) + (x^2 + 1)(3x^2)\\Simplify:\\f'(x) = 2x^4 + 2x + 3x^4 + 3x^2 = 5x^4 + 3x^2 + 2x\\

If you are not familiar with this rule you can first write out the function and then use the basic rule:

f(x) = (x^2 +1)(x^3+1) = x^5 + x^2 + x^3 + 1\\f'(x) = 5x^4 + 2x + 3x^2

If you need any further help please say so in the comments! I hope this helps! If the steps seem complicated, I suggest you could revise expanding brackets (the first step of the second method) and the basic rules of deriving, but feel free to reach out if you struggle afterwards still

8 0
3 years ago
un problema de matemáticas y es así felpe y luis se encontraron en el pedromo para practicar velocidad en bicicleta felpe dijo a
dsp73
I do not know ur language I think it is spanish sorry I couldn't help
3 0
3 years ago
what is the area of a figure what is the area of a figure with a 16 inch base a 10 inch base and a height of 8 in on the left an
tensa zangetsu [6.8K]
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2 years ago
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