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

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

Options:

Correct Answer: 2x + 1

Solution:

f(g(x)) = f(2x) = 2x + 1.

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

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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