Question

what I need for is #2!

#1 is attached for #2.

Please help me! Thanks

1. In class we showed that the function f : R → R given by (if>o 0 if a S0 was smooth (but not real analytic). Note that f(x) approaches a horizontal asymptote (y = 1) as a goes to positive infinity. (a) Show that f(x)+f(1-2)メ0 for all x E R, so that g : R → R given by g(x)- 70 is also a smooth function. (b) Prove that if 0 ifx-1. (c) Note that g()-.Show that the graph of g has order two rotational symmetry about the point (2) by showing that the function g:R- R given by g))s Use this information to sketch the function g. (d) Use the fact that is odd to show that g(x) + g(1-2) = 1 for all x E R. Interpret this with a sketch 2. Let h : R-+ R be the smooth function given by h(z) g is as in Problem 1 g(z + 2g(2-x) for all r E R, where (a) Show that if a

Answer 1

first complete question according to HomeworkLib policy.

a) lesa) far for for x S2-0 & ニ0 2くくく-」 thus gla-)- 32 2-x くy fo &1く2- T= () 3くx+2く4 fei So +5 alaz)