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Math Help - Inversing an equation.

  1. #1
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    Inversing an equation.

    Hi, I need help inversing this function:

    y = 2^(x+1) - 3

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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Tracer View Post
    Hi, I need help inversing this function:

    y = 2^(x+1) - 3

    Swap y with x and x with y to get:

    x = 2^{y+1} - 3

    x+3 = 2^{y+1}

    log(x+3) = log(2^{y+1})

    log(x+3) = (y+1) \mbox{log(2)}

    \frac{log(x+3)}{log2} = y+1

    y = \frac{log(x+3)}{log2}-1
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  3. #3
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    Thanks. But I need help with one more thing. I'm confused with the following problems:

    You purchase a used car for $8,000. The value of the car decreases 20% each year. Approximatively how much is the car worth in five years?

    Find the inverse of: f(x) =

    Lastly; A license plate must have two letters, followed by 3 digits and followed by 2 letters. How many possible license plates are there if letters I and O are excluded and letters and number can be repeated.

    Thanks.
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  4. #4
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    Quote Originally Posted by Tracer View Post
    Thanks. But I need help with one more thing. I'm confused with the following problems:

    You purchase a used car for $8,000. The value of the car decreases 20% each year. Approximatively how much is the car worth in five years?

    Thanks.
    V(n) = 8000\times 0.8^n

    make n=5


    Quote Originally Posted by Tracer View Post

    Find the inverse of: f(x) =
    Like shown in post #2. You need to swap x and y then solve for y.

    y=\sqrt{x-9}

    then

    x=\sqrt{y-9}

    x^2=y-9

    x^2+9=y

    y=x^2+9


    Quote Originally Posted by Tracer View Post
    Lastly; A license plate must have two letters, followed by 3 digits and followed by 2 letters. How many possible license plates are there if letters I and O are excluded and letters and number can be repeated.

    Thanks.
    There are 24 letters and 10 digits available. And they have the order LL DDD LL

    What next?
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  5. #5
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    Quote Originally Posted by harish21 View Post
    Swap y with x and x with y to get:

    x = 2^{y+1} - 3

    x+3 = 2^{y+1}

    log(x+3) = log(2^{y+1})

    log(x+3) = (y+1) \mbox{log(2)}

    \frac{log(x+3)}{log2} = y+1

    y = \frac{log(x+3)}{log2}-1
    I would say

    x = 2^{y+1} - 3

    x +3= 2^{y+1}

    \log_2(x +3)= y+1

    \log_2(x +3)-1= y

    y=\log_2(x +3)-1
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  6. #6
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    Thank you guys. I'm doing a final packet - finals are coming up so I just need sample problems. Our book doesn't show ALL of the examples in this packet - I just forgot some. Ummm.

    A number is selected from 1 to 50. What is the probability that chosen number is prime given that it is less than 31?

    A group has 6 men and 7 women. How many ways can a committee of 2 men and women be formed?

    A red die and a blue die are tossed. What is the probability that a red die will show a 6 and the blue die will show an even number?


    Sorry I suck at probabilities \:
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  7. #7
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    Quote Originally Posted by Tracer View Post

    A number is selected from 1 to 50. What is the probability that chosen number is prime given that it is less than 31?
    First find the probabilty of getting a prime then find the probabilty of a number less then 31.

    What do you get?
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  8. #8
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    Quote Originally Posted by pickslides View Post
    V(n) = 8000\times 0.8^n

    make n=5
    Uhhhh wait where does the 20% go?

    And I got uhhh... 10/50 - 1/5
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  9. #9
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    Quote Originally Posted by Tracer View Post
    Uhhhh wait where does the 20% go?
    20% decrease is the same as multiplying something by 80% or 0.8
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