Question

what is the difference between the function 2^x and (1/2)^x?

Answer 1

well, (1/2) = 2^-1

go to wolframalpha.com and enter

plot y=2^x, y=(1/2)^x

Answer 2

Oh ok! so 2^x is the inverse of (1/2)^x

Answer 3

the difference between the function 2^x and (1/2)^x

= |2^x - (1/2)^x|
= | 2^x - 2^-x |

Answer 4

Oh I wrote the question incorrect. It's not to find the difference but to explain the difference between the two functions

Answer 5

then go with Steve's suggestion and plot the two curves
y = 2^x and y=(1/2)^x to see the result

http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex+%2C+y+%3D+%281%2F2%29%5Ex

Answer 6

2^x is not the inverse of (1/2)^x
log_2(x) is the inverse of 2^x
log_1/2(x) is the inverse of (1/2)^x

You can check this because if g(x) is the inverse of f(x), f(g(x)) = x and g(f(x)) = x

(1/2)^x = 1/2^x
they are reciprocals, not inverses.