Thank you for your patience! Let's analyze the expressions you've listed in relation to the previous function calculation, which resulted in \((f + g)(x) = -2\):
The expressions you provided are:
- \(2^n - 5x + 1\)
- \(2^n + 5x + 1\)
- \(2^n - x - 1\)
- \(2^n - 5x - 1\)
From the previous calculation, we found:
\[
(f + g)(x) = -2
\]
Now we want to determine which of the choices equals \(-2\).
-
For \(2^n - 5x + 1\), set it equal to \(-2\):
\[
2^n - 5x + 1 = -2 \implies 2^n - 5x = -3
\]
(This does not necessarily imply \(2^n - 5x + 1 = -2\) for all \(n, x\))
-
For \(2^n + 5x + 1\):
\[
2^n + 5x + 1 = -2 \implies 2^n + 5x = -3
\]
(Same reasoning)
-
For \(2^n - x - 1\):
\[
2^n - x - 1 = -2 \implies 2^n - x = -1 \implies 2^n = x - 1
\]
(This also depends on \(n\) and \(x\), not equal to \(-2\))
-
For \(2^n - 5x - 1\):
\[
2^n - 5x - 1 = -2 \implies 2^n - 5x = -1 \implies 2^n = 5x - 1
\]
(Again, this does not universally equal \(-2\) for all \(n, x\))
None of these expressions are equal to a constant \(-2\) without additional context or specific values for \(n\) and \(x\).
If you need to select one based on the functional equality rather than just simply being \(-2\), it would still depend on those variable conditions.
Conclusion: If your task is to find if any of these expressions equal \(-2\) for some \(n\) and \(x\), none would directly do so without context. Let me know if you want to consider specific values for \(n\) or \(x\) in the options!