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Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is _________
  • a)
    6x + 9
  • b)
    6x + 7
  • c)
    6x + 6
  • d)
    6x + 8
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let f and g be the function from the set of integers to itself, define...
The composition of f and g is given by f(g(x)) which is equal to 2(3x + 4) + 1.
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Community Answer
Let f and g be the function from the set of integers to itself, define...
First, let's find the composition of f and g, denoted as f(g(x)):

f(g(x)) = f(3x - 4)

Now, substitute the expression for g(x) into f:

f(g(x)) = f(3x - 4) = 2(3x - 4) + 1

Simplify the expression:

f(g(x)) = 6x - 8 + 1

Combine like terms:

f(g(x)) = 6x - 7

Therefore, the composition of f and g is 6x - 7.

Now let's compare this with the given options:

a) 6x - 9: This option is not equal to the composition of f and g (6x - 7).

b) 6x - 7: This option is equal to the composition of f and g (6x - 7).

c) 6x - 6: This option is not equal to the composition of f and g (6x - 7).

d) 6x - 8: This option is not equal to the composition of f and g (6x - 7).

Therefore, the correct answer is option 'A' (6x - 7).
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Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is _________a)6x + 9b)6x + 7c)6x + 6d)6x + 8Correct answer is option 'A'. Can you explain this answer?
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