Mathematics: What is the inverse of the function of (x)=2^(x)+6 a. ^(-1)(x)=6+log_(2)x b. f^(-1)(x)=log_(2)(x+6) c. f^(-1)(x)=6log_(2)x d. f^(-1)(x)=log_(2)(x-6)

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What is the inverse of the function of (x)=2^(x)+6

merunikitty1226

17.01.2022

Option D.

Step-by-step explanation:

To find the inversion of a function follow the following procedure

1) Replace x with y in the function and clear y

$y=2^{(x)} + 6$ ------> $x = 2^{(y)}+ 6$

x-6 = 2^y

y = log_2(x-6)

2) Check. The range of f(x) is the domain of $f^{-1}(x)$ .

So if f(a) = b, this means that $f^{-1}(b)$ = a.

f(2) = 2^2+ 6 = 10

$f^{-1}(x) = log_2(10-6) = 2$

Is fulfilled. Therefore y=log_2(x-6) is the inverse of $f(x) = 2^{(x)} +6$

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