Let the function f:R→R satisfy f(x+z)=f(x)+f(z) for every
x,z∈R
a. Show f(nx)=nf(x) for every n∈Z and x∈R.
b. Prove : if f is continuous at 0, then f is continuous at
every x∈R.
Let the function f:R→R satisfy f(x+z)=f(x)+f(z) for every x,z∈R a. Show f(nx)=nf(x) for every n∈Z and x∈R. b. Prove : if
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Let the function f:R→R satisfy f(x+z)=f(x)+f(z) for every x,z∈R a. Show f(nx)=nf(x) for every n∈Z and x∈R. b. Prove : if
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