Answered

What is the inverse of the function?
f(x) = 3^x + 1

f^-1(x)= log3 (x) +1
f^-1(x)= log3(x)-1

f^-1(x)=log3(x+1)

f^-1(x)=log3(x-1)

Answer :

Answer:

f^-1(x)=logs3(x+1)

Step-by-step explanation:

Let y=f(x)

[tex]\\ \rm\Rrightarrow y=3^x+1[/tex]

  • Interchange

[tex]\\ \rm\Rrightarrow x=3^y+1[/tex]

[tex]\\ \rm\Rrightarrow lnx=ln(3^y+1)[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{ln(y-1)}{ln3}[/tex]

Again interchange

[tex]\\ \rm\Rrightarrow f^{-1}(x)=\dfrac{ln(x-1)}{ln3}[/tex]

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