If g(x)=f(x+k), what is the value of k?

Answer 1

look at g(x)=f(x+k). if f has an inverse in the domain of x+k,

x+k=f^-1(g(x))

k=f^-1(g(x))-x

example: if x is between 0 and 90 degreess

then cos(x)= sin(k-x)= -sin(x-k),

sin^-1(cos(x)=x-π/2=x-k

k=π/2

Answer 2

one solution is k=0

g(x) = f(x+k) if k=0, then g(x) = f(x)

depending on the particular functions, there may be more solutions.

such as g(x) = sinx and f(x) = sin(x+2pi) or sin(x+2npi) where n= any integer

then k=2pi or 2npi where n= any integer