https://file.aiquickdraw.com/mathbot/file/1729409919584qjdo81p0.jpg

The problem presented is an inequality:

\[
f(x) > g(x), \text{ where } f(x) = x^2 + 4 \text{ and } g(x) = 7.
\]

We need to solve this inequality:

\[
x^2 + 4 > 7.
\]

### Step-by-Step Solution:

1. Start by solving the inequality \( x^2 + 4 > 7 \):
   \[
   x^2 + 4 > 7
   \]
   Subtract 4 from both sides:
   \[
   x^2 > 3.
   \]

2. Now, solve \( x^2 > 3 \). This inequality means that \( x \) cannot be between \( -\sqrt{3} \) and \( \sqrt{3} \). In interval notation, the solution is:
   \[
   (-\infty, -\sqrt{3}) \cup (\sqrt{3}, +\infty).
   \]

3. Approximating \( \sqrt{3} \approx 1.732 \), we can conclude that the inequality holds for \( x \in (-\infty, -1.732) \cup (1.732, +\infty) \).

4. Now, let's match this solution to the provided options:
   - Option a: \( (-\infty, 0) \)
   - Option b: "kitas atsakymas" (another answer)
   - Option c: \( (0, +\infty) \)
   - Option d: \( (1, +\infty) \)

The correct solution is not covered precisely by any of the listed intervals, but the closest match in terms of the interval on the positive side is option **d: \( (1, +\infty) \)**, though this does not capture the full range of \( x \). Thus, the correct response seems to be **option b: "kitas atsakymas"**, as it refers to "another answer."

Would you like further clarification on any step or detail?

### Related Questions:
1. How would the solution change if \( g(x) \) was a different constant, say 6?
2. What is the graphical interpretation of the solution \( f(x) > g(x) \)?
3. How would you solve this inequality if \( f(x) = x^2 - 2x + 3 \)?
4. Can we solve this inequality using factorization techniques?
5. How does the solution change if the inequality is \( f(x) \geq g(x) \)?

### Tip:
Always visualize inequalities by plotting the functions \( f(x) \) and \( g(x) \) on a graph—it helps understand the solution intervals better!

Išspręskite nelygybę f(x) > g(x), kai: f(x) = x^2 + 4, o g(x) = 7.

Learn how to solve the inequality f(x) > g(x), where f(x) = x^2 + 4 and g(x) = 7. This step-by-step guide includes solving quadratic inequalities and finding the correct intervals. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation