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Math Help - Critical Thinking with Functions

  1. #1
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    Post Critical Thinking with Functions

    Hello, I'm new to the forum and would like to get some help with two problems that both relate to analyzing functions. I understand the basic concepts but these questions have been placed under the category of "critical thinking" and I'm not sure how to go about solving them.

    Problem #1

    If f(2m+1)=24m^3+36m^2+26m, what is f(x)?
    (Hint: Begin by solving x=2m+1 for m.)

    I tried this, and so far I got m= \frac {-1}{2} for the "hint". I'm not sure if that's what I was supposed to try to figure out, and if it is, I'm not sure where to go from that point.

    Problem #2

    P(x) is a function for which P(1)=1, P(2)=2, P(3)=3, and P(x+1)= \frac {P(x-2)P(x-1)+1}{P(x)} for x \geq 3. Find the value of P(6).

    To be honest, I don't know where to start with this one. I don't know how to deal with all the information that the question is giving me.
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  2. #2
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    Re: Critical Thinking with Functions

    Quote Originally Posted by sararose View Post
    Hello, I'm new to the forum and would like to get some help with two problems that both relate to analyzing functions. I understand the basic concepts but these questions have been placed under the category of "critical thinking" and I'm not sure how to go about solving them.

    Problem #1

    If f(2m+1)=24m^3+36m^2+26m, what is f(x)?
    (Hint: Begin by solving x=2m+1 for m.)

    I tried this, and so far I got m= \frac {-1}{2} for the "hint". I'm not sure if that's what I was supposed to try to figure out, and if it is, I'm not sure where to go from that point.
    What happened to the "x"? m would equal -1/2 if x were equal to 0. Instead, from 2m- 1= x, 2m= x- 1, m= (x- 1)/2. Now replace m by that:
    f(2m+1)=24m^3+36m^2+26m so
    f(x)= 24\frac{(x-1)^3}{2^3}+ 36\frac{(x-1)^2}{2^2}+ 26\frac{x-1}{2}.


    Problem #2

    P(x) is a function for which P(1)=1, P(2)=2, P(3)=3, and P(x+1)= \frac {P(x-2)P(x-1)+1}{P(x)} for x \geq 3. Find the value of P(6).

    To be honest, I don't know where to start with this one. I don't know how to deal with all the information that the question is giving me.
    If x= 3, x+1= 4, x-1= 2, and x-2= 1 so according to that formula, P(4)= \frac{P(1)P(2)+ 1}{P(3)}. Now that you know P(4), what is P(5)?
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  3. #3
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    Re: Critical Thinking with Functions

    Thank you very much! Following your explanation for Question #2, P(5) would be \frac {P(2)P(3)+1}{P(4)}, and by succession P(6) would be \frac {P(3)P(4)+1}{P(5)}, correct?
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  4. #4
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    Re: Critical Thinking with Functions

    Quote Originally Posted by sararose View Post
    Thank you very much! Following your explanation for Question #2, P(5) would be \frac {P(2)P(3)+1}{P(4)}, and by succession P(6) would be \frac {P(3)P(4)+1}{P(5)}, correct?
    Yes, now what are the numerical values?
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