Questions: Suppose f(x)=3x^2-x+9. Compute the following: A.) f(-1)+f(4)= B.) f(-1)-f(4)=

Transcript text: Suppose $f(x)=3 x^{2}-x+9$. Compute the following: A.) $f(-1)+f(4)=$ $\square$ B.) $f(-1)-f(4)=$ $\square$

Solution

Step 1: Evaluate $f(x_1)$ and $f(x_2)$

To find $f(x_1)$, substitute $x_1 = -1$ into the quadratic function $f(x) = 3x^2 - x + 9$, which gives $f(x_1) = 3(-1)^2 - 1(-1) + 9 = 13$.

Similarly, to find $f(x_2)$, substitute $x_2 = 4$ into the function, which gives $f(x_2) = 3(4)^2 - 1(4) + 9 = 53$.

Step 2: Compute $f(x_1) + f(x_2)$

Adding the values of $f(x_1)$ and $f(x_2)$, we get $f(x_1) + f(x_2) = 13 + 53 = 66$.

Step 3: Compute $f(x_1) - f(x_2)$

Subtracting $f(x_2)$ from $f(x_1)$, we get $f(x_1) - f(x_2) = 13 - 53 = -40$.

The sum $f(x_1) + f(x_2) = 66$ and the difference $f(x_1) - f(x_2) = -40$.

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