evaluate or solve composed functions, and in which order?

[mika0]

30. The function A (d ) gives the pain level on a scale of 0-10 experienced by a patient with d milligrams of pain reduction drug in their system. The milligrams of drug in the patient's system after t minutes is modeled by m (t ). To determine when the patient will be at a pain level of 4, you would need to:

a. Evaluate A (m (4))
b. Evaluate m (A (4))
c. Solve A (m (t )) = 4
d. Solve m (A (d )) = 4

I need your help,I'll be very appreciate if you solve this problem

 

[Ishuda]

30. The function A (d ) gives the pain level on a scale of 0-10 experienced by a patient with d milligrams of pain reduction drug in their system. The milligrams of drug in the patient's system after t minutes is modeled by m (t ). To determine when the patient will be at a pain level of 4, you would need to:

a. Evaluate A (m (4))
b. Evaluate m (A (4))
c. Solve A (m (t )) = 4
d. Solve m (A (d )) = 4

I need your help,I'll be very appreciate if you solve this problem

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

As a hint what is d [the amount of pain reduction drug in their system] after 1 minute? Given d at one minute, what is A [their pain level] at one minute?

 

[mika0]

a.evaluate A(m(4))
the argument (input) for the function m(t) is time. 4 is not the time, so this cannot be the correct choice.


b. Evaluate m(A(4))


A(4) is the pain level, not time. the input for the function m(t) is time. So, this choice cannot be correct.


d. Solve m(A(d))=4


A(d) is pain level so this is also incorrect


my answer is C but to tell the truth I cannot make clear explanation why I choose it so can you help me clarify it?

 

[ksdhart]

Perhaps I'm missing something here, because I'm very confused. You say you don't know why you chose answer C... but you also say why the answer can't be any of the other choices Eliminating all the answers that aren't correct is certainly a valid way of reasoning out that the only remaining answer must be correct.

 

[stapel]

30. The function A (d ) gives the pain level on a scale of 0-10 experienced by a patient with d milligrams of pain reduction drug in their system. The milligrams of drug in the patient's system after t minutes is modeled by m (t ). To determine when the patient will be at a pain level of 4, you would need to:

a. Evaluate A (m (4))
b. Evaluate m (A (4))
c. Solve A (m (t )) = 4
d. Solve m (A (d )) = 4

a.evaluate A(m(4))

the argument (input) for the function m(t) is time. 4 is not the time, so this cannot be the correct choice.

So you're saying that the "4" stands for "pain level" while the input "t" of "m" is "time, in minutes", which means that this expression is non-sensical, within the context of the exercise. I agree.

b. Evaluate m(A(4))

A(4) is the pain level, not time. the input for the function m(t) is time. So, this choice cannot be correct.

Yes, "A" (the output here) stands for the level of pain. The input to "A" is "d", the number of milligrams. Since "4" stands for "pain level", not "milligrams", then using the pain-level value as the input is, again, non-sensical. I agree.

d. Solve m(A(d))=4

A(d) is pain level so this is also incorrect

More to the point, the input of "m" is "t", which is time, in minutes. The output of "A" is "pain level", so using A(d) (that is, using the pain level) is non-sensical as an input for "m" (which needs time input). I agree.

my answer is C but to tell the truth I cannot make clear explanation why I choose it so can you help me clarify it?

Use the same kind of reasoning as in the above:

You are given an end-value, being A = 4, the target pain level. So you have been given that A(something) = 4, because A spits out pain-level values, and 4 is the target pain-level value.

You are asked to find "when", which is a time. So you are being asked to find a value for "t". Into which function is "t" put? What is the resulting output (in terms of the listed variables and functions, and their definitions)? Is this sensible, within the context? Also, is this a valid and sensible input for "A"?

And so forth.