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How to Find the Inverse of a Function

If : A→B and...

Question

If : A→B and g : B →C be two functions. Then, composition of f and g, gof : A→C is defined as

A

(gof)(x) = f(x), for all x ∈ A

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B

(gof)(x) = g(f(x)), for all x ∈ A

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C

(gof)(x) = f(g(x)), for all x ∈ A

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D

(gof)(x) = g(x), for all x ∈ A

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Solution

The correct option is B
(gof)(x) = g(f(x)), for all x ∈ A

By definition, composition of f and g, gof is defined as (gof)(x) = g(f(x)), for all x ϵ A.

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f : X \to Y

g : Y \to X

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f (x) = a x + b and g (x) = c x + d, a \neq 0, c \neq 0.

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