For each value of y greater than 23, the function f(x) is

Question

For each value of  y  greater than  2 \sqrt{3} , the function  f(x)  is such that the equation  f(x) = y  has a solution of the form  x=\frac{y^2+12}{y}

Select one value for  a  and one value for  b  such that the given information implies  f(a) = b . Make only two selections, one in each column.

Sajjad1994 · Accepted Answer

Official Explanation

The formula may only be applied for y greater than  2\sqrt{3} , therefore, the only choices available for b are 4, 6, and 8.

If f(a) = b and b = 4, then, according to the formula,

a=\frac{4^2+12}{4}=\frac{28}{4}=7

Since 7 is not an option, b = 4 must not be part of the correct response.

If f(a) = b and b = 6, then, according to the formula,

a=\frac{6^2+12}{6}=\frac{48}{6}=8

Since 8 is an option, a = 8 and b = 6 must be the correct response.

The correct answer is 8.

The correct answer is 6.

CAMANISHPARMAR · Answer

2 \sqrt{3}  is less than 4 because  \sqrt{3}  is less than 2.

Hence:
a = 8 and b = 6

scc404 · Answer

doesn't that mean it has to be greater than 2 because it is 2 and a root which leaves the other numbers? I'm still confused by that.

CAMANISHPARMAR · Answer

Could you please elaborate more on your question; I have not understood it.

lacabral · Answer

I am confused as to how we got b=4. If I plug in 4 for "b", the answer is 7. However, if I plug in a=4, and b=6, the answer becomes f(4)=4. 
Where did I go wrong?

CAMANISHPARMAR · Answer

You may be right, I did not like the question so much. Did you mean to say "a = 8 and NOT 4"? b = 6 seems to be ok. kindly show your calculations.

lacabral · Answer

Yes! Correct, I meant to type a=8, b=6. Thank you so much!

MichaelWunsch · Answer

I am confused as to how we got b=4

AnishPassi · Answer

A few things I noted while reading the question:

1.  2√3 is slightly less than 4. 
2√4 = 4. So, 2√3 would be slightly less.

2.  x will be greater than y. 
The given equation can be simplified to x = y + y/12
Since y is positive, x will be greater than y.

3.
The function is written in the form of 'y = <some function of x>', but the equation is then in the form of 'x = 'some expression in terms of y'

I needed a moment to ensure I processed it correctly.

The given equation in terms of x and y is essentially an elaboration of the relation between x and y. f(x) = y tells us that there is a relation between x and y. What that relation is we get from the equation.

4.  'a' maps to 'x' and 'b' maps to 'y' 
I realized that I could mix up the two constants and end up getting the answer wrong. So, I spent extra time to ensure I understood what a and b represent.

f(x) = y
maps with
f(a) = b
So, 'a' maps to 'x' and 'b' maps to 'y'.

Since I had already understood that x > y, 
I realize a > b.

When I look at the table

1. I can reject 1 and 2 in b's column. Since y > 2√3
2. I can reject 8 for b. Since a > b, so b can't have the highest value.
3. I have 2 options left for b. 4 and 6. I can plug them in.

i. b = 4
x = y + 12/y

if b = 4,
a = 4 + 12/4 
a = 4 + 3 = 7.

7 isn't an option for a.

Reject 4 for b.

---

If I were running short on time at this point, I could directly mark b = 6 and a = 8 at this point.

Why a = 8?

Because a > b. So, if b = 6 (which is the only feasible value left for b), a has to be greater than 6. That leaves only one choice for a.

---

ii. b = 6
x = y + 12/y

if b = 6,
a = 6 + 12/6
a = 6 + 2
a = 8.

a = 8, b = 6.

chetan2u · Answer

x=\frac{y^2+12}{y}  or   a=\frac{b^2+12}{b}=b+\frac{12}{b}

Surely a>b and  b>2\sqrt{3}>2 .
Also, both a and b are even. 
 a=b+\frac{12}{b}  means 12/b is even as even = even + 12/b

12/4 =3...Discard
12/6 = 2..Yes

so  8=6+(\frac{12}{6})

sayan640 · Answer

KarishmaB   MartyMurray  Would you like to explain this question ?

KarishmaB · Answer

Some questions of DI have odd wording but you can figure out what to do by reading what is given and what is asked. 
I struggled to understand what this means:  the function  f(x)  is such that the equation  f(x) = y  has a solution of the form  x=\frac{y^2+12}{y}

but  I ignored it. I could see that there is a relation between x and y if f(x) = y and that's all I cared about because I was given f(a) = b. This  meant that the relation will exist for a and b

a=\frac{b^2+12}{b} = b  + \frac{12}{b}

y needs to be greater than 2*sqrt3 which means that b needs to be greater than 2*1.7 = 3.4 approx.

If b = 4, a = 4 + 3 = 7 (Not available in options)
If b = 6, a = 6 + 2 = 8 - Available

ANSWER: 8, 6

sayan640 · Answer

Thank you  KarishmaB  maa'm.

Posted from my mobile device

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For each value of y greater than 23, the function f(x) is

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For each value of y greater than 23, the function f(x) is

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