Let A = {1, 2, 3, 4} and Z be the set of integers. Define f:A→Z by f(x) = 3x + 7. Show that f is a function from A to Z. Also find the range of f.
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Hi Bro,
A = { 1, 2, 3, 4 }
Z = { ... 1, 2, 3, 4, ... }
f(x) = 3x + 7
f(1) = 3(1) + 7 = 10
f(2) = 3(2) + 7 = 13
f(3) = 3(3) + 7 = 16
f(4) = 3(4) + 7 = 19
Refer the arrow diagram in the attachment. I have proved that the function from from A=>Z is defined. As, each element of A is mapped to Z. It is a One-One function which is also known as injective function.
Range = { 10, 13, 16, 19 }
A = { 1, 2, 3, 4 }
Z = { ... 1, 2, 3, 4, ... }
f(x) = 3x + 7
f(1) = 3(1) + 7 = 10
f(2) = 3(2) + 7 = 13
f(3) = 3(3) + 7 = 16
f(4) = 3(4) + 7 = 19
Refer the arrow diagram in the attachment. I have proved that the function from from A=>Z is defined. As, each element of A is mapped to Z. It is a One-One function which is also known as injective function.
Range = { 10, 13, 16, 19 }
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Answer:
range is { 10,13,16,19}
f = { (1,10),(2,13),(3,16),(4,19)}
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