Question

What is the Inverse function for f(x)=2^(-x) ??

Answer 1

Pls show steps for obtaining the inverse so that I can understand the process...

Answer 2

any idea?

Answer 3

I do not have any idea for such exponential functions....that is why I have put it out...

Answer 4

2^(-x)=?

Answer 5

will it be some logarithmic function???

Answer 6

yep

Answer 7

$$
f(x)=2^{-x} \implies \color{red}{y} = 2^{-\color{blue}{x}}\\
\text{its inverse will be, switching about the letters}\\
f^{-1} \implies \color{blue}{x} = 2^{-\color{red}{y}}
$$

Answer 8

thnks.@jdoe0001

Answer 9

HappySoul to get the inverse of any function, just do a quick switcharoo on the letters, and then solve by "y" usually, don't have to

Answer 10

are you sure about this answer as I have no way of checking it....

Answer 11

lemme solve for "y"

Answer 12

and yes, is a logarithmic function, you use the log cancellation rule, gimme one sec

Answer 13

well, is a logarithmic if you solve for "y" :)

Answer 14

\( \large {
x = 2^{-y} \implies log_2(x) = log_2(2^{-y})\\
log_2(x) = y
} \)

Answer 15

@jdoe0001 thanks for help with explanation...I'll wait for your explanation...

Answer 16

which of the two is correct???

Answer 17

log cancellation rule \(\color{red}{log_n(n^m) = m}\)

Answer 18

they're both correct
\( x = 2^{-y} \) is in exponential notation
\(log_2(x) = y\) is in logarithmic notation

Answer 19

thanks Jdoe0001 for being patient and explaining....

Answer 20

yw

Answer 21

hmmm

Answer 22

ok, let's not forget the exponential was -y :/

Answer 23

\(\large {
x = 2^{-y} \implies log_2(x) = log_2(2^{-y})\\
log_2(x) = -y
}\)

Answer 24

so I guess that'd give \(\large {
-log_2(x) = y
}\)