Respuesta :

meerkat18
We are asked in the problem to determine f−1(2) given the function f(x) = log3 (x + 1). The first step is to determine the inverse of f(x).

f-1(x) :

y = log3(x+1)
x= log3(y+1)
3^x = y +1
y = 3^x - 1
if x = 2 
y = 8

Answer:

Option B. 8

Step-by-step explanation:

Given function is [tex]f(x)=log_{3}(x + 1)[/tex]

Now we have to find the value of [tex]f^{-1}(x)[/tex].

Since [tex]f(x)= y=log_{3}(x+1)[/tex]

[tex]3^{y}=(x + 1)[/tex]

Now for [tex]f^{-1}(x)[/tex]

we will replace x by y.

[tex]3^{x}=y + 1[/tex]

[tex]y=3^{x}-1[/tex]

[tex]f^{-1}(x)=3^{x}-1[/tex]

Now we put the value of x = 2

y = 3²- 1 = 9-1 = 8

Therefore [tex]f^{-1}(2)=8[/tex] is the answer.