7.1 Functions Defined on General Sets Example 7.1.1 A Function Defined by an Arrow Diagram Let X a, b, c and Y= 1,2, 3, 4 Define a function f from X to Y by arrow diagram a. Write the domain and co-domain of f b. Find f(a), f(b), and f(c) 1 c. What is the range off? 2 b d. Is c an inverse image of 2?, Is b an inverse image of 3 e. Find the inverse image of 2, 4, and 1 4 f. Representf as a set of ordered pairs adomain off {a, b, c}, co-domain off = {1,2, 3,4} b f(a)-2, f(b)-4, f(c)=2 range off 2,4 dYes, No Inverse image of2 = { a, c }, Inverse image of 4= {b}, Inverse image of 1 = {} (a, 2), ( b, 4 ), ( c, 2 ) }

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