GMAT Focus Functions Question

[bryan22583]

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?

[rintoo22]

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.

[srcc25anu]

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

[Anju@Gurome]

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.

[Brent@GMATPrepNow]

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