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3 years ago

Composition of functions

1 answer:

7 0

For example, in the composition of(f g)(x) = f(g(x)), we need to replace each x found in f(x), the outside function, with g(x), the inside function. Step 3: Simplify the answer. Examples – Now let's use the steps shown above to work through some examples. Example 1: If f(x) = –4x + 9 and g(x) = 2x – 7, find(f g)(x).

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Write a recursive formula and an explicit formula for the following arithmetic sequence.

xenn [34]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

aₙ₊₁ = aₙ+2, for n ≥1

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2$

The difference between all the adjacent terms is the same and equal to

$d=2$

also

$a_1=11$

so substituting $d=2$ , $a_1=11$ in the nth terms

$a_n=a_1+\left(n-1\right)d$

$a_n=2\left(n-1\right)+11$

$a_n=2n+9$

Therefore, the Explicit formula is:

$a_n=2n+9$

4 0

3 years ago

Use ratio language to describe the relationship between 2 dogs: 1 cat

GenaCL600 [577]

2:1
..................

8 0

3 years ago

Read 2 more answers

Beau and Bellas Grandmother gave them a big box of pencils for school. If they split the pencils equally, what equation shows ho

lions [1.4K]

The answer would be C (P=T/2). This can be explained by examining the ratio. If you were to put in the answer of T = 12, then you would be looking for T/2 or 6, assuming we're giving them each half of the amount original held by grandmother.

5 0

4 years ago

1. Determine el valor de W en las proporciones siguientes:<br> a) (12/w) = (4/3); w =

8090 [49]

Aplicando multiplicación cruzada, tiene-se que el valor de w es w = 9.