Questions: Consider the following piecewise-defined function. f(x) = 2x^2 + 2x + 2 if x ≤ 1 1/3 x + 1 if x > 4 Evaluate this function at x=1. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". f(1)=

Consider the following piecewise-defined function.
f(x) = 
2x^2 + 2x + 2 if x ≤ 1
1/3 x + 1 if x > 4


Evaluate this function at x=1. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

f(1)=
Transcript text: Consider the following piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll} 2 x^{2}+2 x+2 & \text { if } x \leq 1 \\ \frac{1}{3} x+1 & \text { if } x>4 \end{array}\right. \] Step 3 of 3: Evaluate this function at $x=1$. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". Answer Keypad Keyboard Shortcuts Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. \[ f(1)= \] $\square$ Undefined
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Solution

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Solution Steps

Step 1: Determine the condition that x=1 satisfies.

Given the conditions ['x <= 1', 'x > 4'], x=1 satisfies the condition: x <= 1.

Step 2: Apply the corresponding function expression.

The function expression under this condition is \(g_1(x)\).

Calculation:

\(g_1(1) = 6\)

Final Answer:

The value of the piecewise-defined function at x=1 is 6.

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