- #1
KLscilevothma
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Let f:[rr]--> [rr]
It isn't a homework problem.
Let f:[rr]--> [rr] be a function such that f(xy)=f(x)+f(y) for all x,y belong to real numbers
a) Show that for all integers n, f(xn)=nf(x)
b) Suppose the inverse of f exists. Show that for all integers n, [f-1(x)]n=f-1(nx)
I know how to do part (a) but not part (b). Could someone please give me some hints/solution. I can't do problems involving "inverse of a function" unless they are very simple, like to find f-1 of f(x)=(1-x)/(1+x) where x does not equal to 1 or -1
It isn't a homework problem.
Let f:[rr]--> [rr] be a function such that f(xy)=f(x)+f(y) for all x,y belong to real numbers
a) Show that for all integers n, f(xn)=nf(x)
b) Suppose the inverse of f exists. Show that for all integers n, [f-1(x)]n=f-1(nx)
I know how to do part (a) but not part (b). Could someone please give me some hints/solution. I can't do problems involving "inverse of a function" unless they are very simple, like to find f-1 of f(x)=(1-x)/(1+x) where x does not equal to 1 or -1
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