https://file.aiquickdraw.com/mathbot/file/1726683667875l6zlzjin.jpg

The piecewise function given in the image is:

\[
j(x) = 
\begin{cases} 
x^2 - 1 & \text{if } x < 1 \\
4x - 2 & \text{if } x \geq 1
\end{cases}
\]

We are asked to find the value of \( j(x) \) at \( x = 1 \).

Since \( x = 1 \) satisfies \( x \geq 1 \), we use the second part of the piecewise function:

\[
j(x) = 4x - 2
\]

Substituting \( x = 1 \):

\[
j(1) = 4(1) - 2 = 4 - 2 = 2
\]

Therefore, the value of \( j(x) \) at \( x = 1 \) is \( \boxed{2} \).

Would you like more details or have any further questions?

Here are five related questions:
1. How would the value of \( j(x) \) change if \( x = 0.5 \)?
2. How can you find the derivative of this piecewise function?
3. What happens to \( j(x) \) as \( x \to -\infty \)?
4. How would you find the integral of \( j(x) \) from \( x = 0 \) to \( x = 2 \)?
5. Can you describe the continuity of the function \( j(x) \) at \( x = 1 \)?

**Tip:** For piecewise functions, always check which condition the given \( x \) value satisfies to select the correct part of the function.

What is the value of j(x) at x = 1 for the piecewise function j(x) = {x^2 - 1 if x < 1, 4x - 2 if x >= 1}?

Discover how to evaluate the piecewise function j(x) at x = 1 with our in-depth solution. This function consists of two parts: 'x^2 - 1' for x < 1 and '4x - 2' for x >= 1. The evaluation reveals that j(1) equals 2. This analysis is suited for students in Grades 9 to 12, enhancing their understanding of algebra and function evaluation.

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