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The problem in the image asks to find the value of \( b \) such that the function \( f(x) \) is continuous at \( x = 0 \). The function is given as:

\[
f(x) = \begin{cases}
\frac{4x^2 - 7x}{3x}, & \text{if } x \neq 0 \\
b, & \text{if } x = 0
\end{cases}
\]

To ensure continuity at \( x = 0 \), the limit of \( f(x) \) as \( x \to 0 \) must equal the function value at \( x = 0 \), which is \( b \). Thus, we need to compute:

\[
\lim_{x \to 0} f(x) = f(0) = b
\]

### Step 1: Simplify \( f(x) \) for \( x \neq 0 \)

The expression for \( f(x) \) when \( x \neq 0 \) is:

\[
f(x) = \frac{4x^2 - 7x}{3x}
\]

Simplify this:

\[
f(x) = \frac{x(4x - 7)}{3x} = \frac{4x

Consider the function f(x) = { (4x^2 - 7x)/3x if x ≠ 0, b if x = 0 }. If f is continuous at x = 0, find the value of b.

This problem involves finding the value of b such that the piecewise function f(x) is continuous at x = 0. It requires understanding limits, continuity, and simplifying rational functions. Suitable for students in Grades 10-12.

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