Solve f(x)=x² When f(4)=6+a: Function Evaluation Problem

Q: Why do I need to calculate f(4) first instead of just using 4?

The function $ f(x) = x^2 $ tells you to square the input. So $ f(4) = 4^2 = 16 $, not just 4. You must follow the function rule!

Q: What if I forgot to square the 4?

If you use 4 instead of 16, you'd get $ 4 = 6 + a $, giving $ a = -2 $ - which is wrong! Always apply the function rule completely before solving.

Q: How do I know which side of the equation to solve for a?

Once you have $ 16 = 6 + a $, just isolate a by subtracting 6 from both sides. The goal is to get a by itself on one side.

Q: Can I check my answer by plugging it back in?

Yes! Substitute $ a = 10 $ back: $ 6 + 10 = 16 $ and $ f(4) = 16 $. Both sides equal 16, so your answer is correct!

Q: What if the function was different, like f(x) = 2x + 1?

Same process! Calculate $ f(4) = 2(4) + 1 = 9 $, then set $ 9 = 6 + a $ to find $ a = 3 $. Always evaluate the function first!

Function Evaluation with Algebraic Equations

Calculate the value of $a$ .

$f(x)=x^2$

$f(4)=6+a$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find A

00:05 Substitute appropriate values according to the given data, and solve for A

00:21 Calculate the exponent

00:24 Isolate the unknown A

00:32 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

Calculate the value of $a$ .

$f(x)=x^2$

$f(4)=6+a$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate $f(4)$ using the given function.
Step 2: Set $f(4)$ equal to $6 + a$ and solve for $a$ .

Now, let's work through each step:

Step 1: The function given is $f(x) = x^2$ . We want to find $f(4)$ , which is:

$f(4) = 4^2 = 16$

Step 2: According to the problem, $f(4) = 6 + a$ . Therefore, we set:

$16 = 6 + a$

Subtract 6 from both sides to solve for $a$ :

$16 - 6 = a$

$a = 10$

Therefore, the value of $a$ is $a = 10$ .

Final Answer

$a=10$

Key Points to Remember

Essential concepts to master this topic

Function Rule: Substitute input value into function formula first
Technique: Set $f(4) = 4^2 = 16$ equal to $6 + a$
Check: Verify $f(4) = 16$ and $6 + 10 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Setting up the equation incorrectly
Don't write $4 = 6 + a$ instead of evaluating the function first = wrong answer $a = -2$ ! You must calculate $f(4)$ using the function rule before setting up your equation. Always evaluate the function completely, then set it equal to the given expression.

Practice Quiz

Test your knowledge with interactive questions

Complete:

The missing value of the function point:

$$ f(x)=x^2 $$

$$ f(?)=16 $$

FAQ

Everything you need to know about this question

Why do I need to calculate f(4) first instead of just using 4?

The function $f(x) = x^2$ tells you to square the input. So $f(4) = 4^2 = 16$ , not just 4. You must follow the function rule!

What if I forgot to square the 4?

If you use 4 instead of 16, you'd get $4 = 6 + a$ , giving $a = -2$ - which is wrong! Always apply the function rule completely before solving.

How do I know which side of the equation to solve for a?

Once you have $16 = 6 + a$ , just isolate a by subtracting 6 from both sides. The goal is to get a by itself on one side.

Can I check my answer by plugging it back in?

Yes! Substitute $a = 10$ back: $6 + 10 = 16$ and $f(4) = 16$ . Both sides equal 16, so your answer is correct!

What if the function was different, like f(x) = 2x + 1?

Same process! Calculate $f(4) = 2(4) + 1 = 9$ , then set $9 = 6 + a$ to find $a = 3$ . Always evaluate the function first!

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