Choosing Continuous Branches
Difficulty: Hard · Topics: Algebra, Functions, Continuity
Uzluksiz tarmoqlarni tanlash
The function f(x) is continuous in the set of all real numbers and satisfies
\f(x)\^3-\f(x)\^2-x^2f(x)+x^2=0
When the maximum value of f(x) is 1 and the minimum value is 0, evaluate f≤ft(4/3 )+f(0)+f≤ft(1/2 ).
f(x) funksiya barcha haqiqiy sonlar to‘plamida uzluksiz va
\f(x)\^3-\f(x)\^2-x^2f(x)+x^2=0
shartni qanoatlantiradi. f(x) ning eng katta qiymati 1, eng kichigi 0 bo‘lsa, f≤ft(4/3 )+f(0)+f≤ft(1/2 ) ni hisoblang.