To solve for f(1), we start with the given equation:
f(x) = 2f(x^4) + 18
We know from the problem statement that:
f(1) = 2
Now, let’s plug in x = 1 into the function:
f(1) = 2f(1^4) + 18
Since 1^4 = 1, we can simplify this to:
f(1) = 2f(1) + 18
Now, substituting our known value of f(1) = 2 into the equation:
2 = 2(2) + 18
This simplifies to:
2 = 4 + 18
As we can see, this does not hold true, indicating that we’ve made a mistake in our assumption or interpretation. In fact, we can rearrange our original equation:
f(1) – 2f(1) = 18
This gives:
-f(1) = 18
Thus:
f(1) = -18
Thereby concluding that:
- f(1) = -18
Therefore, there was an inconsistency with our assumption that f(1) = 2. The correct value derived through analysis is that f(1) = -18.