Solve f(x)=x²: Finding the Input Value When f(x)=25

Q: Why does x² = 25 have two solutions?

Because both 5² = 25 and (-5)² = 25! When you square a negative number, you get a positive result. So both 5 and -5 work as inputs.

Q: How do I know which answer choice to pick?

Look at the given answer choices carefully. Even though both x = 5 and x = -5 are mathematically correct, you need to select the choice that matches one of the provided options.

Q: What if the number under the square root isn't perfect?

If $ x^2 = 7 $, then $ x = \pm\sqrt{7} $. You can leave it in radical form or use a calculator to find the decimal approximation.

Q: Can I just guess and check the answer choices?

While that might work, it's better to solve algebraically first. Then use the choices to verify your work and see which format they want.

Q: What does f(5) mean exactly?

$ f(5) $ means 'the function f evaluated at x = 5'. So $ f(5) = 5^2 = 25 $. The 5 goes inside the function, and 25 comes out!

Quadratic Functions with Square Root Solutions

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=25$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:04 We'll substitute appropriate values according to the given data, and solve for X

00:12 Extract the root

00:17 When extracting a root there are 2 solutions, positive and negative

00:23 These are the 2 points

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 missing value of the function point:

$f(x)=x^2$

$f(?)=25$

Step-by-step solution

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

Step 1: Set up the equation based on the function $f(x)=x^2$ for $f(?)=25$ .
Step 2: Solve for $x$ by applying the square root operation.

Now, let's work through each step:
Step 1: We start with the equation $x^2 = 25$ derived from $f(x) = 25$ .
Step 2: To solve for $x$ , we take the square root of both sides:

$x = \pm \sqrt{25}$

Calculating the square root gives us $x = \pm 5$ . However, we are looking for a specific point that fits one of the answer choices:
Therefore, the solution based on the choices provided is $x = 5$ .

Concluding, the missing value of the function point is $f(5)$ , which coincides with choice 1.

Final Answer

$f(5)$

Key Points to Remember

Essential concepts to master this topic

Setup: Replace f(x) with given value to create equation
Technique: Take square root of both sides: $\sqrt{25} = 5$
Check: Verify by substituting: $f(5) = 5^2 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting both positive and negative solutions
Don't ignore that $x^2 = 25$ gives both $x = 5$ and $x = -5$ = missing valid solutions! Many students only consider positive roots. Always remember that squaring eliminates the sign, so both positive and negative values work.

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 does x² = 25 have two solutions?

Because both 5² = 25 and (-5)² = 25! When you square a negative number, you get a positive result. So both 5 and -5 work as inputs.

How do I know which answer choice to pick?

Look at the given answer choices carefully. Even though both x = 5 and x = -5 are mathematically correct, you need to select the choice that matches one of the provided options.

What if the number under the square root isn't perfect?

If $x^2 = 7$ , then $x = \pm\sqrt{7}$ . You can leave it in radical form or use a calculator to find the decimal approximation.

Can I just guess and check the answer choices?

While that might work, it's better to solve algebraically first. Then use the choices to verify your work and see which format they want.

What does f(5) mean exactly?

$f(5)$ means 'the function f evaluated at x = 5'. So $f(5) = 5^2 = 25$ . The 5 goes inside the function, and 25 comes out!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve f(x)=x²: Finding the Input Value When f(x)=25

Quadratic Functions with Square Root Solutions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does x² = 25 have two solutions?

How do I know which answer choice to pick?

What if the number under the square root isn't perfect?

Can I just guess and check the answer choices?

What does f(5) mean exactly?

🌟 Unlock Your Math Potential

More Questions

Parabola of the form y=x²

Square Diagonal Formula: Finding Length in Terms of Side 'a'

Solve f(x) = x²: Finding the Missing Value When f(x) = 16

Calculate the Area Function: Shaded Triangle in a Square with Side Length a

Solve f(x) = x²: Finding the Input Value When f(?) = 49