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?
GMAT Focus Functions Question
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f(x) = 2^x - 3bryan22583 wrote:The function f is defined by f(x) = (2^x) -3. If f(x) = 31, the the value of x is between:
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.
Anju Agarwal
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Given: f(x) = 2^x - 3bryan22583 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
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