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What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?

Practice Questions

Q1
What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?
  1. 2x + 1
  2. 2x - 1
  3. x + 2
  4. x + 1

Questions & Step-by-Step Solutions

What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?
  • Step 1: Identify the functions given. We have f(x) = x + 1 and g(x) = 2x.
  • Step 2: To find the composition f(g(x)), we need to replace g(x) in the function f(x).
  • Step 3: Substitute g(x) into f(x). This means we replace x in f(x) with g(x), which is 2x.
  • Step 4: Write down the new function: f(g(x)) = f(2x).
  • Step 5: Now, apply the function f to 2x. Since f(x) = x + 1, we replace x with 2x in this expression.
  • Step 6: Calculate f(2x): f(2x) = 2x + 1.
  • Step 7: Therefore, the final answer is f(g(x)) = 2x + 1.
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