SOLUTION: If f(x) = log3 (x + 1), what is f−1(2)? A) 1 B) 8 C) 10 D) 27

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If f(x) = log3 (x + 1), what is f−1(2)? A) 1 B) 8 C) 10 D) 27       Log On


   

Question 844373: If f(x) = log3 (x + 1), what is f−1(2)?
A) 1
B) 8
C) 10
D) 27

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%28x%29%22%22%22=%22%22log%283%2C%28x%2B1%29%29


Change f(x) to y

y%22%22=%22%22log%283%2C%28x%2B1%29%29

Interchange x and y

x%22%22=%22%22log%283%2C%28y%2B1%29%29

Use the principle that A=log%28B%2C%28C%29%29 is equivalent to C=B%5EA 

y%2B1%22%22=%22%223%5Ex

Solve for y:

y%22%22=%22%223%5Ex-1

Replace y by f-1(x)

f-1(x) = 3x - 1 

So substitute x=2

f-1(2) = 32 - 1 = 9 - 1 = 8

Edwin