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3 years ago

11

PLEASE HELP

1 answer:

Nastasia [14]3 years ago

5 0

Only if i knew :(((:(((

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

2 years ago

The explicit rule for a sequence is given. an=4n−1 What is the recursive rule for the sequence?

Gnom [1K]

Answer:

$a_{n+1}=a_n+4$

Step-by-step explanation:

Have in mind the definition of the term $a_n=4\,n-1$ , and now work on what the term $a_{n+1}$ is based on the previous definition:

$a_{n+1} = 4\,(n+1)-1\\a_{n+1}=4\,n+4-1$

In the next step do NOT combine the numerical values, but try to identify the $a_n$ term ( $4\,n-1$ ) in the expression (notice the use of square brackets to group the relevant terms):

$a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4$

So now we have the term " $a_{n+1}$ " defined in a recursive manner based on the previous term " $a_n$ "

8 0

3 years ago

How do I do this? I don’t understand

Ganezh [65]

You have to input the 5 into the x place. so it would be y=3(5) and you get the answer y=15

5 0

3 years ago

Read 2 more answers

Lucie has $3.28 in pennies, nickels, dimes and quarters. She has twice as many dimes as nickels and five fewer quarters than dim

Alex_Xolod [135]

Answer:

a dollar 95 my man I did this

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3 years ago

The scale factor from rectangle Y to rectangle Z is 2. Which statement is true?

Neporo4naja [7]

Answer:

Answer is C not A

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3 years ago