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

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
scc404 wrote:
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.

Could you please elaborate more on your question; I have not understood it.
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
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?
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
lacabral wrote:
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?

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.
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
CAMANISHPARMAR wrote:
lacabral wrote:
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?

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.

Yes! Correct, I meant to type a=8, b=6. Thank you so much!
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
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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.

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
I am confused as to how we got b=4
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
­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'.

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.

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
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scc404 wrote:
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.

­ $$x=\frac{y^2+12}{y}$$ 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

12/6 = 2..Yes

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

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
KarishmaB MartyMurray Would you like to explain this question ?
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Re: For each value of y greater than 23, the function f(x) is [#permalink]
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scc404 wrote:
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.

­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

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
Thank you KarishmaB maa'm.

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Re: For each value of y greater than 23, the function f(x) is [#permalink]
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