If f(x) = log3 (x + 1), what is f−1(2)

2 answers:

7 0

Firstly, we'll find y = f⁻¹(x):

$f(x)=\log_3(x+1)\\\\
x=\log_3(y+1)\\\\
y+1=3^x\\\\
y=3^x-1\\\\
f^{-1}(x)=3^x-1
$

So:

$f^{-1}(x)=3^x-1\\\\
f^{-1}(2)=3^2-1\\\\
f^{-1}(2)=9-1\\\\
\boxed{f^{-1}(2)=8}$

saveliy_v [14]3 years ago

4 0

Answer: The value is 8.

Step-by-step explanation: Given function is

$f(x)=\log_3(x+1).$

we are given to find the value of $f^{-1}(2).$

Let us consider that

$f(x)=y~~~~~\Rightarrow x=f^{-1}(y).$

So, we have

$f(x)=\log_3(x+1)\\\\\Rightarrow y=\log_3(f^{-1}(y)+1)\\\\\Rightarrow 3^y=f^{-1}(y)+1\\\\\Rightarrow f^{-1}(y)=3^y-1.$

If y = 2, then we have

$f^{-1}(2)=3^2-1=9-1=8.$

Thus, the required value is 8.

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