Question

which function is the inverse of f(x) =b^x

Answer 1

Answer:

The correct answer is C.

Step-by-step explanation:

To find this, we need to note that in order to reverse the function of raising the b to the x power, we need to take the log base b of the function. Since the answer C is the only one containing that, it must be the correct answer,

Answer 2

The inverse of the given function is expressed as $g^{-1}(y)=log_xb$

Given the exponential function $g(x)=b^x$

Let y = f(x), to have $y = b^x$

Replace y with x to have:

$x=b^y$

Make y the subject of the formula by taking the log of both sides

$logx=logb^y\\logx=ylogb$

Divide both sides by log b

$y=\frac{logx}{log b} \\y = log_xb$

Hence the inverse of the given function is expressed as $g^{-1}(y)=log_xb$

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