The Inverse Function — الرياضيات البحتة الصف الثاني الثانوي لغات

درس «The Inverse Function» فى مادة الرياضيات البحتة لـالصف الثاني الثانوي لغات من وحدة «Unit 2: Exponents, Logarithms and Their Applications». This lesson defines the inverse of a one-to-one function f^(-1), proves the reflection symmetry of the graphs of f and f^(-1) across the line y = x, establishes that domain of f^(-1) equals range of f, and derives inverse rules algebraically. هتتعلم فى الدرس ده: A function f possesses an inverse f^(-1) if and only if f is a one-to-one function.، Domain of f^(-1) = Range of f, and Range of f^(-1) = Domain of f.، The composite relations satisfy: (f ∘ f^(-1))(x) = x and (f^(-1) ∘ f)(x) = x.، Graphically, the curve of y = f^(-1)(x) is the reflection...

الدرس ده من وحدة «Unit 2: Exponents, Logarithms and Their Applications» فى مادة الرياضيات البحتة لـالصف الثاني الثانوي لغات على منصة دروسات.

الدرس متاح بالاشتراك: ترم كامل أو المادة لوحدها.

ملخص الدرس

This lesson defines the inverse of a one-to-one function f^(-1), proves the reflection symmetry of the graphs of f and f^(-1) across the line y = x, establishes that domain of f^(-1) equals range of f, and derives inverse rules algebraically.

هتتعلم إيه فى الدرس ده

• A function f possesses an inverse f^(-1) if and only if f is a one-to-one function.
• Domain of f^(-1) = Range of f, and Range of f^(-1) = Domain of f.
• The composite relations satisfy: (f ∘ f^(-1))(x) = x and (f^(-1) ∘ f)(x) = x.
• Graphically, the curve of y = f^(-1)(x) is the reflection of the curve y = f(x) about the line y = x.
• To find f^(-1)(x) algebraically: swap x and y in y = f(x), then solve for y.