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:

$f(x)=x^2$

$f(?)=25$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's set up the problem and solve it step by step.

00:13 We'll plug in the given values, carefully replacing each variable, to find the value of X.

00:21 Next, we'll extract the root of the equation.

00:26 Remember, when extracting a root, we can have two solutions: p ositive and negative.

00:32 These give us two possible points.

00:39 And that's how we find the solution to our 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

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 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!

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