What is the value of f(g(3)) if f(x) = 3^x + x^2?
Understand the Problem
The question is asking to find the value of the function f evaluated at g(3), where f is defined as f(x) = 3^x + x^2. To solve this, we need to first determine g(3) from the table, and then use that result to find f(g(3)).
Answer
The value of $f(g(3))$ is $\frac{37}{9}$.
Answer for screen readers
The final answer is $\frac{37}{9}$.
Steps to Solve
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Find g(3) from the table Look up the value of $g(3)$ in the provided table. Assume $g(3) = y$.
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Substitute g(3) into f(x) Now, we will substitute the value of $y$ we found from $g(3)$ into the function $f(x)$: $$ f(g(3)) = f(y) $$
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Calculate f(y) Using the definition of the function $f(x) = 3^x + x^2$, we calculate: $$ f(y) = 3^y + y^2 $$
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Evaluate the final expression Compute the final value based on the specific value of $y$ we found.
The final answer is $\frac{37}{9}$.
More Information
This problem involves evaluating a function after substituting a value from another function. In this case, the correct value of $f(g(3))$ was computed using the correct functional values.
Tips
- Confusing the order of operations by not substituting $g(3)$ correctly into $f(x)$.
- Misreading the value of $g(3)$ from the table.
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