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Verified Answer :

syed514

f(x)=0.3(4)^x

f^-1(x) = ?

x = 0.3(4)^y

4^y = x/0.3

4^y = 6/0.3

4^y = 20

y = 2.161

carlosego

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

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