Find Domain of \(f^{-1}\)
🎥 Video Explanation
📝 Question
Let:
\[ f(x)=x^3 \]
Domain of \(f\): \(\{0,1,2,3\}\)
Find domain of \(f^{-1}\).
- (a) \(\{3,2,1,0\}\)
- (b) \(\{0,-1,-2,-3\}\)
- (c) \(\{0,1,8,27\}\)
- (d) \(\{0,-1,-8,-27\}\)
✅ Solution
🔹 Step 1: Find Range of \(f\)
\[ f(0)=0,\quad f(1)=1,\quad f(2)=8,\quad f(3)=27 \]
Range:
\[ \{0,1,8,27\} \] —
🔹 Step 2: Domain of Inverse
Domain of \(f^{-1}\) = Range of \(f\)
—🔹 Final Answer
\[ \boxed{\text{Option (c)}} \]