diff --git a/minitorch/operators.py b/minitorch/operators.py
index 35b5a15..895408d 100644
--- a/minitorch/operators.py
+++ b/minitorch/operators.py
@@ -74,7 +74,7 @@ def sigmoid(x: float) -> float:
     for stability.
     """
     # TODO: Implement for Task 0.1.
-    raise NotImplementedError("Need to implement for Task 0.1")
+    return (1.0 / (1.0 + math.exp(-x))) if x >= 0 else math.exp(x) / (1 + math.exp(x))
 
 
 def relu(x: float) -> float:
@@ -103,7 +103,7 @@ def exp(x: float) -> float:
 def log_back(x: float, d: float) -> float:
     r"If $f = log$ as above, compute $d \times f'(x)$"
     # TODO: Implement for Task 0.1.
-    raise NotImplementedError("Need to implement for Task 0.1")
+    return d / x
 
 
 def inv(x: float) -> float:
@@ -116,7 +116,7 @@ def inv(x: float) -> float:
 def inv_back(x: float, d: float) -> float:
     r"If $f(x) = 1/x$ compute $d \times f'(x)$"
     # TODO: Implement for Task 0.1.
-    raise NotImplementedError("Need to implement for Task 0.1")
+    return -(x ** (-2)) * d
 
 
 def relu_back(x: float, d: float) -> float: