Questions: Find f(-5)=(-2x^2+3x-7)/(x-5)

Transcript text: Find $f(-5)=\frac{-2 x^{2}+3 x-7}{x-5}$

Solution

Solution Steps

To find $ f(-5) $ for the given function $ f(x) = \frac{-2x^2 + 3x - 7}{x - 5} $, we need to substitute $ x = -5 $ into the function and evaluate the expression.

Step 1: Substitute $ x = -5 $ into the function

Given the function $ f(x) = \frac{-2x^2 + 3x - 7}{x - 5} $, we substitute $ x = -5 $:

\[ f(-5) = \frac{-2(-5)^2 + 3(-5) - 7}{-5 - 5} \]

Step 2: Simplify the numerator and denominator

Calculate the numerator:

\[ -2(-5)^2 + 3(-5) - 7 = -2(25) - 15 - 7 = -50 - 15 - 7 = -72 \]

Calculate the denominator:

\[ -5 - 5 = -10 \]

Step 3: Divide the simplified numerator by the denominator

Now, divide the simplified numerator by the denominator:

\[ f(-5) = \frac{-72}{-10} = 7.2 \]

Final Answer

\[ \boxed{7.2} \]

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