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SMUP 2010

Solusi SMUP 2010 Kode 041 – Nomor 10


Diketahui\ f(x)=3^{x+2}-4.\ Jika\ f^{-1}(x)\ adalah\ invers\ dari\ f(x),\\maka\  f^{-1}(5)\ sama\ dengan\ ....\\A.\quad  -2\\B.\quad -1\\C.\quad 0\\D.\quad 1\\E.\quad 2
Jawaban: C

\begin{array} {rcl} y&=&3^{x+2}-4\\\\3^{x+2}&=&y+4\\\\x+2&=&^{3}log(y+4)\\\\x&=&^{3}log(y+4)-2\\\\f^{-1}(y)&=&^{3}log(y+4)-2\\\\f^{-1}(5)&=&^{3}log(5+4)-2\\\\&=&^{3}log(5+4)-2\\\\&=&^{3}log9-2\\\\&=&2-2\\\\&=&0\end{array}

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