Solve f(x)=x² When f(6)=6+a: Finding the Missing Value

To solve this problem, we will follow a methodical approach:

• Step 1: Evaluate $f(6)$ using the function $f(x) = x^2$.
• Step 2: Set $f(6) = 6 + a$ and solve for $a$.

Now, let's apply these steps:
Step 1: Compute $f(6)$. Since $f(x) = x^2$, we have $f(6) = 6^2 = 36$.
Step 2: We are given that $f(6) = 6 + a$. Therefore, substitute the evaluated value:
$36 = 6 + a$.

To find $a$, solve the equation $36 = 6 + a$. Subtract $6$ from both sides:

$36 - 6 = a$ which simplifies to $a = 30$.

Therefore, the solution to the problem is $a = 30$.