inverse functions (please help if u can!)

Question

x 1 2 3 4 5 6

f(x) 1 2 4 8 16 32

a function is given by a table of values, a graph, a formula, or a verbal description. determine whether it is one-to-one.

Answer 1

f(x) = 2^(x-1)

an exponential function, one to one

as it passes the vertical and horizontal line tests, with flying colors

one horizontal asymptote, the x axis or y=0

no vertical asymptotes,

no x intercepts

one y intercept 1 = the point (0,1)

to find the inverse function switch x and f(x)=y and solve for the new y

y = 2^(x-1)

x = 2^(y-1) solve for y to get f^-1(x)

which is also a one to one function

it's just y =2^(x-1) reflected over the line x=y

take logs of both sides, to the base 2

log(2)x = y-1

y = 1 + logx to the base 2

f^-1(x) = 1+log(2)x