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Evgen [1.6K]
3 years ago
8

A sequence is defined by the recursive function f(n+1)=f(n). If f(3)=9, what is f(1)?

Mathematics
2 answers:
vekshin13 years ago
6 0
Put n=2 ,
f(2+1) = f(2) => f(3) = f(2) = 9
now, put n=1,
f(1+1) = f(1) => f(2) = f(1) = 9
shusha [124]3 years ago
5 0

Answer:  The required value of f(1) is 9.

Step-by-step explanation:  Given that a sequence is defined by the following recursive function :

f(n+1)=f(n)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

and f(3) = 9.

We are to find the value of f(1).

Putting n = 2 in equation (i), we have

f(2+1)=f(2)\\\\\Rightarrow f(3)=f(2).

Since f(3) = 9, so we get

f(2)=9.

Again, putting n = 1 in equation (i), we get

f(1+1)=f(1)\\\\\Rightarrow f(2)=f(1).

Since f(2) = 9, so we arrive at

f(1)=9.

Thus, the required value of f(1) is 9.

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This is not a function because some of the x-values repeat, which is not how a function works. For this to be a function, each x-value would have to be different. In this case, the 4 and 5 repeat in the x-values.

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Step-by-step explanation:

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4. Diego is thinking of two positive numbers. He says, "If we triple the first number and
aleksandr82 [10.1K]

Answer:

3<em>x </em>+ 2<em>y</em> = 34. and two possible pairs of positive numbers are  (<em>x</em>, <em>y</em>) = (10, 2) and (<em>x</em>, <em>y</em>) = (4, 11).

Step-by-step explanation:

 Let the First positive number be <em>x</em> and second positive number be <em>y.</em>

Triple of first number = 3<em>x</em>

double of second number = 2<em>y</em>

According to question,

3<em>x </em>+ 2<em>y</em> = 34

Therefore, the equation is 3<em>x </em>+ 2<em>y</em> = 34

So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3<em>x </em>+ 2<em>y</em> = 34

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3<em>x </em>= 34 - 2<em>y</em>

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