To prove that f = g for the given functions f(x) = x + 2 and g(x) = 3x, we need to show that they have the same mapping for all elements in the domain A.
Let's evaluate f(x) and g(x) for each element in A:
For x = 1:
f(1) = 1 + 2 = 3
g(1) = 3(1) = 3
For x = 2:
f(2) = 2 + 2 = 4
g(2) = 3(2) = 6
We can see that for both x = 1 and x = 2, f(x) and g(x) give the same output values.
Therefore, since f(x) = g(x) for all elements in the domain A = {1, 2}, we can conclude that f = g.
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Verified answer
To prove that f = g for the given functions f(x) = x + 2 and g(x) = 3x, we need to show that they have the same mapping for all elements in the domain A.
Let's evaluate f(x) and g(x) for each element in A:
For x = 1:
f(1) = 1 + 2 = 3
g(1) = 3(1) = 3
For x = 2:
f(2) = 2 + 2 = 4
g(2) = 3(2) = 6
We can see that for both x = 1 and x = 2, f(x) and g(x) give the same output values.
Therefore, since f(x) = g(x) for all elements in the domain A = {1, 2}, we can conclude that f = g.
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