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alex41 [277]
3 years ago
14

Simplify pls 8(4x-12)

Mathematics
1 answer:
bija089 [108]3 years ago
4 0

Answer:

32x-96

Step-by-step explanation:

8 · 4x = 32x

8 · 12 = 96

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[Will mark as brainliest]
Aleks04 [339]

The answer is: f^{-1} = 4x^2-3,\quad\text{for  } x \leq 0

The inverse of a function f(x) is another function, f^{-1}(x), with the following property:

f(f^{-1}(x)) = f^{-1}(f(x)) = x

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, f(x)=2x, and one that halves it: f(x)= \frac{x}{2}. Their composition is clearly the identity function f(x)=x, since you consider "twice the half of something", or "half the double of something".

In general, to invert a function y=f(x), you have to solve the expression for x, writing an expression like x = g(y). If you manage to do so, then g is the inverse of f.

In your case, you have

f(x) = y = -\frac{1}{2}\sqrt{x+3}

Multiply both sides by -2 to get

-2y = \sqrt{x+3}

Square both sides to get

4y^2 = x+3

Finally, subtract 3 from both sides to get

x = 4y^2 - 3

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

f^{-1}(x) = 4x^2 - 3

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain b \in B such that there exists a \in A : f(a)=b. So, we need the range of f(x).

We know that the range of g(x)=\sqrt{x} is [0,\infty). When you transform it to g(x)=\sqrt{x+3} you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times -\frac{1}{2} you affect both extrema of the range, turning it into (-\infty,0], which you can simply write as x \leq 0

4 0
3 years ago
The pressure and volume of an expanding gas are related by the formula PV^b=C, where b and C are constants (this holds in adiaba
bazaltina [42]

The dP/dt of the adiabatic expansion is -42/11 kPa/min

<h3>How to calculate dP/dt in an adiabatic expansion?</h3>

An adiabatic process is a process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression

Given b=1.5, P=7 kPa, V=110 cm³, and dV/dt=40 cm³/min

PVᵇ = C

Taking logs of both sides gives:

ln P + b ln V = ln C

Taking partial derivatives gives:

\frac{1}{P}\frac{∂P}{∂t}  + \frac{b}{V}\frac{∂V}{∂t} = 0

Substitutituting the values b, P, V and dV/dt into the derivative above:

1/7 x dP/dt +  1.5/110 x 40 = 0

1/7 x dP/dt +  6/11 = 0

1/7 x dP/dt = - 6/11

dP/dt = - 6/11 x 7

dP/dt = -42/11 kPa/min

Therefore, the value of  dP/dt is -42/11 kPa/min

Learn more about adiabatic expansion on:

brainly.com/question/6966596

#SPJ1

4 0
1 year ago
Pls help BRAINLYEST FOR BEST ANSWER YAYA
son4ous [18]

Answer:

A) 21

Step-by-step explanation:

Mean:

(23 + 18 + 24 + 15 + 25)/5

105/5

21

6 0
3 years ago
Read 2 more answers
Find the volume of a right circular cone that has a height of 8.9 ft and a base with a
xxMikexx [17]

Answer:

1186.16

Step-by-step explanation:

8 0
2 years ago
If a=3 and b=5 then ab/15+a(6+7b)=
lilavasa [31]

Answer:155

Step-by-step explanation:

If a=3 and b=5 then

3•5/15+3•6+7•5=155

8 0
3 years ago
Read 2 more answers
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