25 ++ fjWPbg fB[X R[f ~ 132802
By definition, y ∈ f(A)∩f(B) ⊇ Let y ∈ f(A) ∩ f(B) Then y ∈ f(A) and y ∈ f(B) Thus there exists x 1 ∈ A with f(x 1) = y and there exists x 2 ∈ B with f(x 2) = y By injectivity of f we have x 1 = x 2, and thus x 1 ∈ B, too So x 1 ∈ A ∩ B and hence y = f(x 1) ∈ f(A∩B) 1222 (b) Prove that f(A \ B) = f(A) \ f(B3 Suppose that f R !R is a continuous function such that lim x!1 f(x) = 0;07 N5 ・@ E t F b g ・ Wヲ ・J ・I @0744 X V u 07 N f V ^ O v ・ I @ X V N C X 00C SRT8 ・A ・・・f J ・・・o ・I @ X V Letter Formation The Ot Toolbox fjWPbg fB[X R[f "~