Round #1101
21 May 2026, 09:40· math· Meta-Llama-3.3-70B-Instruct· r13-clean-hints
- Complexity
- band 0
- ZP / UO / OBS
- 3 / 0 / 2
- Journey weight
- 413
- Lightshift ΔL
- —
Prompt
Given f(x) = (x - 4) / 3, state the inverse function f^(-1)(x). Give the inverse in explicit form.
Zero-point index (what the engine surfaced)
ZPI-ZPI-0030 | 2026-05-21T09:40:52Z
Given f(x) = (x - 4) / 3, state the inverse function f^(-1)(x). Give the inverse in explicit form.
ZERO POINT — 3 entries (structural invariants)
● hsl(166.59, 100%, 15%) f∘f^(-1) = f^(-1)∘f = identity [contract]
● hsl(317.35, 100%, 15%) existence requires bijection (one-to-one and onto) [contract]
● hsl(256.81, 100%, 15%) graph reflection across y = x [contract]
UNOBSERVED — 0 entries (implied truths)
OBSERVED — 2 entries (explicit in request)
◉ hsl(151.79, 100%, 15%) / [feature]
◉ hsl(175.38, 100%, 27%) = [feature]
COMPLEXITY │ 5 entries │ spread: 24° │ band: LOW
Baseline response (no ZPI)
## Step 1: To find the inverse function, we first need to replace f(x) with y.
We have y = (x - 4) / 3.
## Step 2: Next, we swap x and y to begin solving for the inverse function.
This gives us x = (y - 4) / 3.
## Step 3: Now, we solve for y to find the inverse function.
First, multiply both sides by 3 to get rid of the fraction: 3x = y - 4.
## Step 4: Then, add 4 to both sides to isolate y.
This results in 3x + 4 = y.
## Step 5: Since we're finding the inverse function, we replace y with f^(-1)(x).
So, the inverse function f^(-1)(x) is 3x + 4.
The final answer is: $\boxed{3x + 4}$
Enhanced response (with ZPI)
To find the inverse function f^(-1)(x), we can swap x and y in the original function and then solve for y.
Given f(x) = (x - 4) / 3, we first rewrite it as y = (x - 4) / 3. Swapping x and y gives x = (y - 4) / 3.
Now, solving for y:
x = (y - 4) / 3
x * 3 = y - 4
x * 3 + 4 = y
So, the inverse function f^(-1)(x) is 3x + 4.
Grader chain
Each grader reads the same baseline + enhanced pair and casts an independent verdict. Disagreement is the framework's own signal — not noise to be averaged away.
V1samba/Meta-Llama-3.3-70B-Instruct
SameV4qwen2.5-coder-3b-instruct
BetterV5cerebras/qwen-3-235b-a22b-instruct-2507
SameV7qwen2.5-coder-7b-instruct
SameV8openai/gpt-4.1
SameV9anthropic/claude-opus-4-7
SameV12openai/gpt-4o
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