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3 years ago

Find the inverse, g−1(x), of the following function: g(x) = 4x - 11

Mathematics

1 answer:

Sphinxa [80]3 years ago

7 0

Answer:

$g^{-1}$ (x) = $\frac{x+11}{4}$

Step-by-step explanation:

let y = g(x) and rearrange making x the subject, that is

y = 4x - 11 ( add 11 to both sides )

y + 11 = 4x ( divide both sides by 4 )

$\frac{y+11}{4}$ = x

Change y back into terms of x , with x = $g^{-1}$ (x) , thus

$g^{-1}$ (x) = $\frac{x+11}{4}$

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A city block has 6 pigeons and then 1 week later there are 9 pigeons. Let P(t)be the number of pigeons where t is measured in we

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Using proportions, it is found that the differential equation which describes the growth of the pigeon population is given by:

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<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the initial population and the population one week later, the rate of growth is given by:

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More can be learned about proportions at brainly.com/question/24372153

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2 years ago

How much more would $1,000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the int

s2008m [1.1K]

Answer: There is a difference of $ 1.0228.

Explanation: Given, initial amount or principal = $ 1000,

Time= 5 years and given compound rate of interest = $3.7%

Now, Since the amount in compound continuously,

$A= Pe^{rt}$ , where, r is the rate of compound interest, P is the principal amount and t is the time.

Here, P=$ 1000, t=5 years and r= $3.7%,

Thus, amount in compound continuously , $A=1000e^{3.7\times5/100}$

⇒ $A=1000e^{18.5}=1000\times 1.20321844013=1203.21844013$

Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013

now, Since the amount in compound quarterly,

$A=P(1+\frac{r/4}{100} )^{4t}$ , where, r is the rate of compound interest, P is the principal amount and t is the time.

Thus, amount in compound quarterly, $A=1000(1+\frac{3.7/4}{100} )^{4\times5}$

⇒ $A=1000(1+\frac{3.7}{400} )^{20}$

⇒ $A= 1202.19567617$

Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617

So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228

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