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ArbitrLikvidat [17]
4 years ago
12

Find the inverse of the given function f(x) =2^x+6

Mathematics
1 answer:
ruslelena [56]4 years ago
8 0

Answer:

f^{-1}(x) = log_2(x-6)

Step-by-step explanation:

To find the inverse f^{-1}(x) of a function follow the following steps.

1) Do y = f (x)

f(x) =y= 2 ^ x + 6

y= 2 ^ x + 6

2) Solve the equation for the variable x.

y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)

3) exchange the variable y with the variable x

x=log_2(y-6)\\\\y=log_2(x-6)

Finally the inverse is:

f^{-1}(x) = log_2(x-6)

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