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2 years ago

Write an equation to represent the sequence 19, 38, 57, 76,95 ...

Mathematics

1 answer:

morpeh [17]2 years ago

8 0

Answer:

Step-by-step explanation:

lets look at the numbers

38-19=19

57-38=19

76-57=19

aₙ=aₙ-₁ +19

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PLEASE HELP!!!!<br> Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

3 0

3 years ago

"mon ame ne suivit pas la sienne"<br><br><br>quelle figure de style represente cette phrase?

just olya [345]

Answer:

It is a metaphor.

Step-by-step explanation:

Hope it helps

3 0

2 years ago

Find slope of both lines and determine if parallel, perpendicular or neither

Oxana [17]

Answer:

Parallel

Step-by-step explanation:

y=5x+10

y=5x-15

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2 years ago

Allison went to the store to buy some walnuts. The price per pound of the walnuts is

spin [16.1K]

Answer:

Step-by-step explanation:

4 0

2 years ago

50 points please help

Ratling [72]

Answer:

A traditional economy is a system that relies on customs, history, and time-honored beliefs. Tradition guides economic decisions such as production and distribution. Societies with traditional economies depend on agriculture, fishing, hunting, gathering, or some combination of them. They use barter instead of money.

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2 years ago

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