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)=
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
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\[
f(1)=
\]
$\square$
Undefined
Solution
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.