If f(n) = xa^n, what is the value of f(5) ?

Target question: What is the value of f(5)?

Given: f(n) = xa^n

Statement 1: f(0) = 3
In other words, x(a^0) = 3
Since a^0 = 1, we can write: (x)(1) = 3
This tells us that x = 3
So, our function now looks like this: f(n) = 3a^n
Since we still don't know the value of a, this is NOT enough information to determine the value of f(5)
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: f(4) = 48
In other words, x(a^4) = 48
There are several values of x and a that satisfy statement 2. Here are two:
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case f(5) = 3(2^5) = 96
Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 3
Statement 2 tells us that, when x = 3, either a = 2 or a = -2
In other words, we still have 2 possible cases that satisfy BOTH statements:
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case f(5) = 3(2^5) = 96
Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E