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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?
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Q1
What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?
2x + 1
2x - 1
x + 2
x + 1
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f(g(x)) = f(2x) = 2x + 1.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?
Solution:
f(g(x)) = f(2x) = 2x + 1.
Steps: 7
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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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