Jika \( f(x)=3^{x-1} \) maka \( f^{-1}(81) = \cdots \)
- 1
- 2
- 3
- 4
- 5
Pembahasan:
Misalkan \(f(x)\) sama dengan \(y\) sehingga diperoleh berikut ini:
\begin{aligned} f(x) = 3^{x-1} \Leftrightarrow y &= 3^{x-1} \\[1em] {}^3 \! \log y &= x-1 \\[8pt] x &= {}^3 \! \log y+1 \\[8pt] f^{-1}(x) &= {}^3 \! \log x+1 \\[8pt] f^{-1}(81) &= {}^3 \! \log 81+1 \\[8pt] &= {}^3 \! \log 3^4+1 \\[8pt] &= 4 \cdot {}^3 \! \log 3 + 1 \\[8pt] &= 5 \end{aligned}
Jawaban E.