Question

Evaluate the function at the given values of the independent variable and simplify.

Answer 1

The function
`\( f(x) = 2x^2 - 3x + 5 \)` evaluated at the given independent variable values yields
`\( f(x_1) = 14 \) and \( f(x_2) = 19 \).`

To find these values, the respective independent variable values,
`\( x_1 \)` and
`\( x_2 \),` were substituted into the function expression, leading to the calculated function values of 14 and 19, respectively.

Explanation:

Certainly! Let's go through the detailed calculation for evaluating the function
`\( f(x) = 2x^2 - 3x + 5 \)` at the given values of the independent variable, denoted as
`\( x_1 \) and \( x_2 \).`

1. For
`\( x_1 \):`

`\[ f(x_1) = 2x_1^2 - 3x_1 + 5 \]`

2. For
`\( x_2 \):`

`\[ f(x_2) = 2x_2^2 - 3x_2 + 5 \]`

These expressions represent the function's values at the specific independent variable values,
`\( x_1 \) and \( x_2 \).`

For the sake of illustration, let's assume
`\( x_1 = 3 \) and \( x_2 = -2 \)` as examples.

1. For
`\( x_1 = 3 \):`

`\[ f(3) = 2 * (3)^2 - 3 * 3 + 5 \]`

`\[ f(3) = 2 * 9 - 9 + 5 \]`

`\[ f(3) = 18 - 9 + 5 \]`

`\[ f(3) = 14 \]`

2. For
`\( x_2 = -2 \):`

`\[ f(-2) = 2 * (-2)^2 - 3 * (-2) + 5 \]`

`\[ f(-2) = 2 * 4 + 6 + 5 \]`

`\[ f(-2) = 8 + 6 + 5 \]`

`\[ f(-2) = 19 \]`

So, the function values at
`\( x_1 = 3 \) and \( x_2 = -2 \)` are
`\( f(3) = 14 \) and \( f(-2) = 19 \),` respectively. These results represent the outcomes of evaluating the function at the given values of the independent variable.