Questions: Evaluate the piecewise function at the given value of the independent variable. f(x)= 4x+3 if x<2 5x+2 if x ≥ 2 f(3)

Solution Steps

To evaluate the piecewise function at \( x = 3 \), we need to determine which part of the function to use based on the condition provided. Since \( x = 3 \) is greater than or equal to 2, we will use the expression \( 4x + 3 \) to find \( f(3) \).

The piecewise function is defined as follows:

• \( f(x) = 5x + 2 \) if \( x < 2 \)
• \( f(x) = 4x + 3 \) if \( x \geq 2 \)

Since we need to evaluate \( f(3) \) and \( 3 \geq 2 \), we use the expression \( 4x + 3 \).

Substitute \( x = 3 \) into the expression \( 4x + 3 \): \[ f(3) = 4(3) + 3 \]

Calculate the value: \[ f(3) = 12 + 3 = 15 \]

Final Answer