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GalinKa [24]
3 years ago
14

If ƒ(x ) = 3x + 1 and ƒ -1 = , then ƒ(2) =

Mathematics
1 answer:
MrRa [10]3 years ago
4 0

Answer:

f(-1)=

\frac{ - 2}{3}

f(2)=

\frac{1}{3}

Step-by-step explanation:

let f(x)=f(-1)

but f(x) =3x+1

substituting it into the equation

3x+1=-1

3x=-1-1

3x=-2

dividing through by 3

\frac{3x}{3}  =  \frac{ - 2}{3}

x =  \frac{ - 2}{3}

f(-1) =

\frac{ - 2}{3}

f(2)

let f( x )=f(2)

then

3x+1=2

3x=2-1

3x=1

dividing through by 3

\frac{3x}{3}  =  \frac{1}{3}

x =  \frac{1}{3}

f(2)=

\frac{1}{3}

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The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

<h3>How to identify a converging or diverging series?</h3>

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

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Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

Read more about converging or diverging series at; brainly.com/question/15415793

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