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

Q: Why can't I just say a = 36 since f(6) = 36?

Because the problem states that f(6) = 6 + a, not f(6) = a. You need to use this condition: since f(6) = 36 and f(6) = 6 + a, then 36 = 6 + a, so a = 30.

Q: What does f(6) actually mean?

f(6) means the output when x = 6. For f(x) = x², substitute 6 for x: f(6) = 6² = 36. It's the value of the function at that input.

Q: How do I solve 36 = 6 + a for a?

Use inverse operations! Since 6 is added to a, subtract 6 from both sides: 36 - 6 = a, so a = 30.

Function Evaluation with Algebraic Equations

Complete:

the value $a$ The subtraction of the function point:

$f(x)=x^2$

$f(6)=6+a$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find A

00:04 Substitute appropriate values according to the given data, and solve for A

00:16 Calculate the exponent

00:26 Isolate the unknown A

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete:

the value $a$ The subtraction of the function point:

$f(x)=x^2$

$f(6)=6+a$

Step-by-step solution

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 $a = 30$ .

Final Answer

$a=30$

Key Points to Remember

Essential concepts to master this topic

Function Rule: Substitute input value into function formula first
Technique: Calculate f(6) = 6² = 36, then solve 36 = 6 + a
Check: Verify f(6) = 36 equals 6 + 30 = 36 ✓

Common Mistakes

Avoid these frequent errors

Setting up equation incorrectly
Don't write a = 6² = 36 directly! This skips the crucial step of using the given condition f(6) = 6 + a. Always evaluate the function first, then set it equal to the given expression to solve for the unknown.

Practice Quiz

Test your knowledge with interactive questions

What is the value of y for the function?

$$ y=x^2 $$

of the point $$ x=6 $$ ?

FAQ

Everything you need to know about this question

Why can't I just say a = 36 since f(6) = 36?

Because the problem states that f(6) = 6 + a, not f(6) = a. You need to use this condition: since f(6) = 36 and f(6) = 6 + a, then 36 = 6 + a, so a = 30.

What does f(6) actually mean?

f(6) means the output when x = 6. For f(x) = x², substitute 6 for x: f(6) = 6² = 36. It's the value of the function at that input.

How do I solve 36 = 6 + a for a?

Use inverse operations! Since 6 is added to a, subtract 6 from both sides: 36 - 6 = a, so a = 30.

Can I check my answer somehow?

Yes! Substitute back: if a = 30, then 6 + a = 6 + 30 = 36. Since f(6) = 36 too, both sides match. Your answer is correct!

What if the function was different, like f(x) = x³?

Same method! Calculate f(6) = 6³ = 216, then solve 216 = 6 + a to get a = 210. The process stays the same regardless of the function.

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