Question

Which function is the inverse of F(x) = b^x?

Answer 1

I'd suggest that you actually find the inverse of the given function, and then compare your result to the four possible answer choices.

If F(x) = b^x, replace "F(x)" with y. Would you do that now, please?

Answer 2

f^(-1) (x) = (log(x))/(log(b))

Answer 3

Now what?

Answer 4

I haven't actually worked this problem through yet, but will do it now. I asked you to replace "F(x)" with y; the resulting equation is y = b^x. You apparently were able to do muhc more than that; your result agrees with mine. Just label it \[F ^{-1}(x)\]
to match up with the original F(x).

Answer 5

Does this correspond to any of the four possible answer choices?

Answer 6

not sure?

Answer 7

I don't know the Socratic way to get to a definition, but this what you need to know:

\( \displaystyle \begin{gather} \text{for } b \ge 0\text{, } b \ne 1 \text{, } \text{ and } y \gt 0 \text{, } \cr y=b^x \iff x = \log_b y \end{gather} \)

And g(x) and f(x) are inverse functions if g(f(x)) = x = f(g(x))

Answer 8

Ah so D?

Answer 9

Yes, I'd go along with that. Note that I obtained the expression\[\frac{ \ln x }{ \ln b }\]

Answer 10

which is part of the "change of base formula."