The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of

Question

The function f(x) is defined by  f(x)=100−2^x . If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4
 
B. 4<x≤8
 
C. 8<x≤16
 
D. 16<x≤32
 
E. 32<x≤64

BrentGMATPrepNow · Accepted Answer

If f(x) = 6, then 100 - 2^x = 6
Rearrange to get: 2^ x  =  94

Observe: 
 2 ^6 =  64 
 2 ^7 =  128

Since  94  is BETWEEN  64  and  128 , we can conclude that  x  is BETWEEN  6  and  7

Only answer choice B meets the criteria that  x  is BETWEEN  6  and  7

Answer: B

Cheers,
Brent

JeffTargetTestPrep · Answer

We are given that f(x) = 100 - 2^x and that f(x) = 6. Thus:

6 = 100 - 2^x

2^x = 94

We are looking for a number such that 2 raised to that number is equal to 94. We know that 2^6 = 64 and 2^7 = 128. Therefore, even though we can’t determine the exact value of x (unless we have a calculator), we know that 6 < x < 7. Since 6 < x < 7, the correct answer choice is B: 4 < x ≤ 8.

Answer: B

Kinshook · Answer

f(x) = 6 = 100 - 2^x
2^x = 94
2^6 = 64
and 2^7 = 128
6<x<7

Only B. 4<x≤8 satisfies the criteria

IMO B

BrushMyQuant · Answer

Given that  f(x)=100−2^x  and f(x)=6 and we need to find the range of values of x

f(x)=100−2^x  = 6 (given)
=>  100−2^x = 6 
=>  2^x = 100 - 6 
=>  2^x = 94 
Now, we know that  2^6 = 64  and  2^7 = 128 
=> x will be between 6 and 7
Only option in that range is 4<x≤8

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

deepak.brijendra · Answer

But this does say that x can be 7 or 8. Which is incorrect value of the equation. The correct value is not in the option.

BrushMyQuant · Answer

Value of x is coming between 6 and 7.
Only the range given in option B where x is between 4 and 8 is containing this range of x is between 6 and 7.
So, that's the correct option choice.

Do you have any other doubt on the same pls?

kaustubhkohli12 · Answer

I got confused here thinking B option says 4<x<=8 , so if x is 8 or 7 , then it will give negative value. Could you help if this logic even make sense or i should just think from where we cann get 94 and ignore other possibilities ?

Bunuel · Answer

Your logic does not apply here.

Option B is not saying that  every  value from 4 to 8 works. It is saying that the actual value of x lies somewhere in that range.

Since 2^x = 94, and 2^6 < (2^x = 94) < 2^7, we know:

6 < x < 7

That range is inside option B: 4 < x <= 8.

So B is correct.

The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of

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The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of

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