Prove that `f(x)=sqrt(|x|-x)` is continuous for all `xgeq0.`

Prove that f(x)=sqrt(|x|-x) is continuous for all x>=0

Prove that f(x)=sqrt(|x|-x) is continuous for all x>=0

Prove that f (x) =|x| is continuous at x =0

Prove that f(x)=|x| is continuous at x=0

Prove that f(x)=|1-x+|x|| is a continuous function at x=0

Prove that f(x)= 2x-|x| is a continuous function at x= 0.

If f((x + 2y)/3)=(f(x) + 2f(y))/3 AA x, y in R and f(x) is continuous at x = 0. Prove that f(x) is continuous for all x in R.

Value of f(0) so that f(x)=(sqrt(2+x)-sqrt(2))/(x) is continuous at x=0 is

If f is a real function such that f(x)>0,f^(prime)(xx) is continuous for all real xa n da xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1.

Prove that the function f(x) =2x-|x| is continuous at x=0.