Use the following function rule to find f(2). f(x) = 11(7)^x
Check the final answer first, then review the worked steps.
Problem
Use the following function rule to find f(2). f(x) = 11(7)^x
Answer
539
Step-by-step solution
- Understand the function rule: The problem provides a function rule $f(x) = 11(7)^x$. This means that for any input value $x$, the output $f(x)$ is calculated by raising 7 to the power of $x$ and then multiplying the result by 11.
- Identify the input value: We are asked to find $f(2)$. This means the input value for $x$ is 2.
- Substitute the input value into the function rule: Replace every instance of $x$ in the function rule with the value 2. This gives us $f(2) = 11(7)^2$.
- Calculate the exponent: First, calculate $7^2$. This means 7 multiplied by itself: $7^2 = 7 imes 7 = 49$.
- Perform the multiplication: Now, substitute the result from the previous step back into the equation: $f(2) = 11(49)$. Finally, multiply 11 by 49: $11 imes 49 = 539$.
- State the final answer: The value of $f(2)$ is 539.