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)

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)
Transcript text: Evaluate the piecewise function at the given value of the independent variable. $f(x)=$ $4 x+3$ if $x<2$ $5 x+2$ if $x \geq 2$ $f(3)$
failed

Solution

failed
failed

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 \( f(3) \).

Step 1: Determine the Appropriate Function Expression

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 \( 4x + 3 \).

Step 2: Substitute the Value into the Expression

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

Step 3: Perform the Calculation

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

Final Answer

\(\boxed{f(3) = 15}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
shown in the
failedAnswered
L= ( 1 0 0 0 1 1 0 0 -3 -1/2 1 0 2 0 -2 1 ) U= ( -1 2 3 1 0 4 -3 5 0 0 1/2 -9/2 0 0 0 12 )
failedAnswered
Multiply. Write your answer in lowest terms. (8-2z)/49 * 98/(7z-28)
failedAnswered
Technical writing oftentimes requires writing in the due to making instructions easier to understand. Informal voice Active voice Formal voice Passive voice
failedAnswered
The diaphragm separates the: mediastinum from the abdominal cavity. pelvic cavity from the abdominal cavity. pericardial cavity from the pleural cavity. mediastinum from the pleural cavity.