When f(x) = 2x and g(x) = x² + 3, find f(g(x)).
Understand the Problem
The question is asking to find the result of the composition of two functions, specifically f(g(x)). We have f(x) defined as 2x and g(x) defined as x² + 3. To solve this, we need to substitute g(x) into f(x).
Answer
$2x^2 + 6$
Answer for screen readers
The final answer is: $2x^2 + 6$.
Steps to Solve
-
Identify the functions
We have two functions defined:
- $f(x) = 2x$
- $g(x) = x^2 + 3$
-
Substitute $g(x)$ into $f(x)$
To find $f(g(x))$, we substitute $g(x)$ into $f(x)$:
$$ f(g(x)) = f(x^2 + 3) $$ -
Apply $g(x)$ to $f(x)$
Now we replace the variable in $f(x)$ with the expression $x^2 + 3$:
$$ f(x^2 + 3) = 2(x^2 + 3) $$ -
Distribute the constant
Distributing the 2:
$$ f(x^2 + 3) = 2 \cdot x^2 + 2 \cdot 3 = 2x^2 + 6 $$
The final answer is: $2x^2 + 6$.
More Information
The composition of functions is a way to combine two functions where the output of one function becomes the input of another. In this case, we see how the results of function $g(x)$ transform when plugged into function $f(x)$.
Tips
- Forgetting to substitute the entire function $g(x)$ into $f(x)$, leading to errors.
- Neglecting to distribute properly can cause mistakes in the final result. Always double-check each step of the arithmetic.
AI-generated content may contain errors. Please verify critical information
