functions

Mohsin,
This has been answered before on this forum. Pls search.

thanks

You can solve this by inserting X and 1-X to each choices and waste your 4 minutes..or since the correct answer will be for all x!

You should use X =1 so 1-X will be 0

just compare the results with x=1 and X=0

this will eliminate A, B and C in 30 seconds!

D looks right but you cant test E with X=1

so just check E with some other alternatives , lets say X=2 and X=-1

and you will see that the answer choices are not the same..but hey I checked the D too with X=2 and X=-1 and ...well I am not sure about the the validity of D & E any more

okay I found the original Q and yes it is D.

This question is begging to plug numbers in.

Plugging 2 into original equation and you get -1 as the target.

A yields -1 hence my answer choice.
B yields -3 no
C yields 3 no
D yields 1 no
E yields -2 no

So where am I going wrong? IMO QA IS A

the ans is D

just substitute 1-x in plce of x in all options
you will easily be ablr to remove all wrong

A
it will turn out to be x which is wrong

B
x^2 will give something like 2x which can not be removed so wrong

C
good choice
but -ve sign will create problem

D
OK

E
easy one
it will becme 1-x/x

I am trying your way, however, I am very apt to plug in numbers to bring about concrete answers. My brain is wired that way. I dont see how my answer is wrong!

simba12123 wrote:I am trying your way, however, I am very apt to plug in numbers to bring about concrete answers. My brain is wired that way. I dont see how my answer is wrong!

For must be true questions, use numbers to prove that particular option is WRONG.

simba12123 wrote:This question is begging to plug numbers in.

Plugging 2 into original equation and you get -1 as the target.

A yields -1 hence my answer choice.

Plugging 2 gives -1 as the answer
that means we need to prove that
f(2) = f(-1)

but what you are concluding it as
f(2) = -1
Which is wrong.



f(x) = 1-x
so
f(1-x)
=1-(1-x)
=x

remember
x ! f(x)

B yields -3 no
C yields 3 no
D yields 1 no
E yields -2 no

So where am I going wrong? IMO QA IS A

Received a PM for detailed reply.
Here I go.............


I will try for option A, rest you do yourself and let me know if you want me to do those as well.


Method 1: Without numbers
we need to prove f(x) = f(1-x) for all x

A
f(x) = 1-x

now if f(1-x) is also equal to 1-x than I can say A is the answer.

Let me try
we know
f(x) = 1-x

substitute x by 1-x
f(1-x) = 1-(1-x) = 1-1+x = x

Now we know
f(x) = 1-x
and
f(1-x) = x
so f(x) != f(1-x)
hence A can not be the answer....


Method 2: With numbers
you choose x = 2
so f(2) = 1-2 = -1

now we need ot prove that
f(2) = f(1-2) ie
f(2) = f(-1) [what you are proving is f(2) = -1, which is not desired. We want f(2) to be equal to f(-1)]

now let me do
f(-1)
ie substitute x by -1 in f(x) = 1-x
f(-1) = 1-(-1) =2

hence
when x = 2
f(x) != f(1-x)
as f(2) is -1 and f(-1) is 2
so we can say A is incorrect.

Please do this for all other options, the concept will become clear to you.

Stop@800

I get it! I usually tend to make things more complex than they really are. I saw one step that was in my way of clarity. I thank you and stand correct. The main takeaway from this is not a mechanical error approach but more of a framing issue. I must step back before jumping into the computations to see what is really being asked. I am now one step closer to my 700. Thankyou

simba12123 wrote:Stop@800

I get it! I usually tend to make things more complex than they really are. I saw one step that was in my way of clarity. I thank you and stand correct. The main takeaway from this is not a mechanical error approach but more of a framing issue. I must step back before jumping into the computations to see what is really being asked. I am now one step closer to my 700. Thankyou

True for everyoe.