Questions: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) f(x)=x^2+9x f(0)= 0 f(3)= 36 f(-3)=-18 f(a)=a^2 f(-x)= x^2 f(1/a)=1/a^2+7/a

Transcript text: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) \[ \begin{array}{l} f(x)=x^{2}+9 x \\ f(0)= 0 \\ f(3)= 36 \\ f(-3)=-18 \\ f(a)=a^{2} \\ f(-x)= x^{2} \\ f\left(\frac{1}{a}\right)=\frac{1}{a^{2}}+\frac{7}{a} \end{array} \]

Solution

Solution Steps

To evaluate the function \( f(x) = x^2 + 9x \) at the indicated values, substitute each value into the function and simplify. If the result is undefined, return "UNDEFINED".

Step 1: Evaluate \( f(0) \)

Substitute \( x = 0 \) into the function \( f(x) = x^2 + 9x \): \[ f(0) = 0^2 + 9 \times 0 = 0 \]

Step 2: Evaluate \( f(3) \)

Substitute \( x = 3 \) into the function: \[ f(3) = 3^2 + 9 \times 3 = 9 + 27 = 36 \]

Step 3: Evaluate \( f(-3) \)

Substitute \( x = -3 \) into the function: \[ f(-3) = (-3)^2 + 9 \times (-3) = 9 - 27 = -18 \]

Step 4: Symbolic Evaluation of \( f(a) \)

For \( f(a) \), substitute \( x = a \): \[ f(a) = a^2 + 9a \]

Step 5: Symbolic Evaluation of \( f(-x) \)

For \( f(-x) \), substitute \( x = -x \): \[ f(-x) = (-x)^2 + 9(-x) = x^2 - 9x \]

Step 6: Symbolic Evaluation of \( f\left(\frac{1}{a}\right) \)

For \( f\left(\frac{1}{a}\right) \), substitute \( x = \frac{1}{a} \): \[ f\left(\frac{1}{a}\right) = \left(\frac{1}{a}\right)^2 + 9\left(\frac{1}{a}\right) = \frac{1}{a^2} + \frac{9}{a} \]