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GMAT Focus Functions Question

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by bryan22583 » Tue Apr 16, 2013 12:37 pm
The function f is defined by f(x) = (2^x) -3. If f(x) = 31, the the value of x is between:

(A) 1 and 2
(B) 2 and 3
C) 3 and 4
(D) 4 and 5
(E) 5 and 6

Anyone know how to solve this?
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by rintoo22 » Tue Apr 16, 2013 12:49 pm
f(x) = (2^x) -3 and f(x) = 31
Therefore 31 = (2^x)-3
consider x=5, then (2^5)-3 = 29
consider x=6, then (2^6)-3 = 61

31 falls between 29 and 61. Hence the answer should be E.
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by srcc25anu » Tue Apr 16, 2013 2:07 pm
f(x) = 2^x - 3 = 31
2^x = 34
we know 2^5 = 32 and 2^6 = 64
since 34 lies in between 32 and 64, x must be between 5 and 6
hence E
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by Anju@Gurome » Tue Apr 16, 2013 8:59 pm
bryan22583 wrote:The function f is defined by f(x) = (2^x) -3. If f(x) = 31, the the value of x is between:
f(x) = 2^x - 3
As, f(x) = 31 ---> 2^x = (31 + 3) = 34

Now, powers of 2 are : 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32,...

As 2^x = 34 > 32 = 2^5, x must be greater than 5.

Only possible option is E.

The correct answer is E.
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by Brent@GMATPrepNow » Sat Oct 19, 2019 1:51 pm
bryan22583 wrote:The function f is defined by f(x) = (2^x) -3. If f(x) = 31, the the value of x is between:

(A) 1 and 2
(B) 2 and 3
C) 3 and 4
(D) 4 and 5
(E) 5 and 6
Given: f(x) = 2^x - 3
So, if f(x) = 31, we can write: 2^x - 3 = 31
Add 3 to both sides to get: 2^x = 34 [solve this equation for x]

We know that 2^5 = 32
and 2^6 = 64
Since 34 lies between 32 and 64, we can conclude that x is between 5 and 6

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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