Solving functions ques

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greatchap: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sun May 04, 2008 12:23 am; Location: India; Thanked: 1 times

Solving functions ques

by greatchap » Fri Nov 19, 2010 11:20 pm

Hi Guys,

Inspite of some search, I am unable to determine how to solve questions with functions ?

For e.g.

If function f(x) satisfies f(x)=f(x^2) for all x, which of the following must be true?

(A) f(4)=f(2) f(2)
(B) f(16)-f(2)=0
(C) f(-2)+f(4)=0
(D) f(3)=3f(3)
(E) f(0)=0

I don't know where to start ?

Please help me out here.

Thanks,

GR

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Source: Beat The GMAT — Problem Solving | Fri Nov 19, 2010 11:20 pm

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 am; Location: Bangalore, India; Thanked: 146 times; Followed by:24 members

by shovan85 » Sat Nov 20, 2010 12:09 am

greatchap wrote: If function f(x) satisfies f(x)=f(x^2) for all x, which of the following must be true?

(A) f(4)=f(2) f(2)
(B) f(16)-f(2)=0
(C) f(-2)+f(4)=0
(D) f(3)=3f(3)
(E) f(0)=0

IMO B

f(x)=f(x^2) for all x

A: Incorrect
f(2) = f(2^2) = f(4)
And f(2) * f(2) = [f(2)]^2

Thus f(4) = f (2) and not f(4) = f(2)*f(2)

B: Correct
f(2) = f(2^2) = f(4)
f(4) = f(4^2) = f(16)
Thus f(2) = f(16) => f(16)-f(-2) = 0

C: Incorrect
f(-2) = f([-2]^2) = f(4)
Thus, f(-2) - f(4) = 0 Not f(-2)+f(4)=0

D: Incorrect
f(3) = f(3^2) = f(9)
Thus f(3) = f(9)
But there is no way to say f(9) = 3f(3)

E: Incorrect
f(0) = f(0^2) but we do not know what is f(0) from the Question.
So we cannot say f(0) = 0

As per solving, see the question what is given as the function. Here f(x) = f(x^2) for all x.
Then go to each option take one side either LHS or RHS of the eqn and expand it as per the condition given in Q.
Once you reach or cross the other side after expansion then compare with the other side and make a decision.
See here after B I would not have bothered about rest as B is concretely correct.

If the problem is Easy Respect it, if the problem is tough Attack it

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greatchap: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sun May 04, 2008 12:23 am; Location: India; Thanked: 1 times

by greatchap » Sat Nov 20, 2010 4:02 am

Thanks for your help buddy.

Though I got a hang of it but to understand it better, can I illustrate -

B: Correct
f(2) = f(2^2) = f(4)
f(4) = f(4^2) = f(16)
Thus f(2) = f(16) => f(16)-f(-2) = 0

So here f(16)=f(4)=f(2) so thats why result is 0 right?

but if we solve last choice f(0)=0 then isnt it true- as f(0)=f(0^2) which is 0.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Nov 20, 2010 4:09 am

greatchap wrote:Hi Guys,

Inspite of some search, I am unable to determine how to solve questions with functions ?

For e.g.

If function f(x) satisfies f(x)=f(x^2) for all x, which of the following must be true?

(A) f(4)=f(2) f(2)
(B) f(16)-f(2)=0
(C) f(-2)+f(4)=0
(D) f(3)=3f(3)
(E) f(0)=0

I don't know where to start ?

Please help me out here.

Thanks,

GR

Scan the answers, looking for one that's easy to prove.

Answer choices A and B discuss f(2). Let's start there.

The problem stipulates that f(x) = f(x^2) for all values of x. This means that:

f(2) = f(2^2) = f(4)
So f(2) = f(4)

f(4) = f(4^4) = f(16)
So f(4) = f(16)

Thus, f(2) = f(4) = f(16).

So we can prove answer choice B: f(16) - f(2) = 0.

The correct answer is B.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Nov 20, 2010 4:17 am

greatchap wrote:Thanks for your help buddy.

Though I got a hang of it but to understand it better, can I illustrate -

B: Correct
f(2) = f(2^2) = f(4)
f(4) = f(4^2) = f(16)
Thus f(2) = f(16) => f(16)-f(-2) = 0

So here f(16)=f(4)=f(2) so thats why result is 0 right?

but if we solve last choice f(0)=0 then isnt it true- as f(0)=f(0^2) which is 0.

We don't know the actual function itself. We know only the relationship between x values of the function: that, for all values of x, f(x) = f(x^2).

If x=0, we know that f(0) = f(0^2) = f(0), but we don't know the actual value of f(0).

Last edited by GMATGuruNY on Sat Nov 20, 2010 4:22 am, edited 2 times in total.

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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 am; Location: Bangalore, India; Thanked: 146 times; Followed by:24 members