For this case we have the following function:
[tex]f (x) = 0.3 (4) ^ x
[/tex]
Rewriting we have:
[tex]y = 0.3 (4) ^ x
[/tex]
From here, we clear the value of x:
[tex](4) ^ x = y / 0.3
log4 ((4) ^ x) = log4 (y / 0.3)[/tex]
Rewriting we have:
[tex]x = log4 (y / 0.3)
[/tex]
Therefore, the inverse function is given by:
[tex]f ^ {-1} (x) = log4 (x / 0.3)
[/tex]
For x = 6 we have:
[tex]f ^ {-1} (6) = log4 (6/0.3)
f ^ {-1} (6) = 2.161[/tex]
Answer:
is the value of f^-1(6) is:
c. 2.161
