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If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?

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Question: If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?

Options:

  1. 4
  2. 9
  3. 16
  4. 25

Correct Answer: 9

Solution: 

(f ∘ g)(2) = f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.

If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?

Practice Questions

Q1
If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?
  1. 4
  2. 9
  3. 16
  4. 25

Questions & Step-by-Step Solutions

If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?
  • Step 1: Identify the functions. We have f(x) = x^2 and g(x) = x + 1.
  • Step 2: Find g(2). Substitute 2 into g(x): g(2) = 2 + 1.
  • Step 3: Calculate g(2). This gives us g(2) = 3.
  • Step 4: Now, we need to find f(g(2)), which is f(3).
  • Step 5: Substitute 3 into f(x): f(3) = 3^2.
  • Step 6: Calculate f(3). This gives us f(3) = 9.
  • Function Composition – Understanding how to combine two functions, where the output of one function becomes the input of another.
  • Evaluation of Functions – Calculating the value of a function at a specific point.
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