If f: A → B and g: B → C are one-one functions show that gof is a one-one function.

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If f: A → B and g: B → C are one-one functions, show that g o f is a one-one function. If f: A → B and g: B → C are one-one functions, show that g o f is a one-one function.
Composite Functions Composite Functions
Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one) Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)
In each of the following cases, state whether function is one-one, onto or bijective f:R-R f(x)=3-4x In each of the following cases, state whether function is one-one, onto or bijective f:R-R f(x)=3-4x
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS
If f and g are two bijections; then gof is a bijection and `(gof)^-1 = f^-1 o g^-1` If f and g are two bijections; then gof is a bijection and `(gof)^-1 = f^-1 o g^-1`
gof: A TO C IS BIJECTION PROOF. COMPOSITE FUNCTION OF f and g. INTER FIRST YEAR MATHS gof: A TO C IS BIJECTION PROOF. COMPOSITE FUNCTION OF f and g. INTER FIRST YEAR MATHS
One to one and onto functions | Relations and Functions | Class XII | Mathematics | Khan Academy One to one and onto functions | Relations and Functions | Class XII | Mathematics | Khan Academy