Questions: For the function (f(x)=frac-3 x+3-5 x-6), evaluate (f(2)). [ f(2)= ]

$For the function (f(x)=frac-3 x+3-5 x-6), evaluate (f(2)). [ f(2)= ]$

Transcript text: For the function $f(x)=\frac{-3 x+3}{-5 x-6}$, evaluate $f(2)$. \[ f(2)= \] $\square$ Submit Try another version of this question

Solution

Solution Steps

To evaluate the function $ f(x) = \frac{-3x + 3}{-5x - 6} $ at $ x = 2 $, substitute $ x = 2 $ into the function and simplify the expression to find the value of $ f(2) $.

Step 1: Substitute $ x = 2 $ into the function

We start with the function: \[ f(x) = \frac{-3x + 3}{-5x - 6} \] Substituting $ x = 2 $: \[ f(2) = \frac{-3(2) + 3}{-5(2) - 6} \]

Step 2: Simplify the numerator and denominator

Calculating the numerator: \[ -3(2) + 3 = -6 + 3 = -3 \] Calculating the denominator: \[ -5(2) - 6 = -10 - 6 = -16 \]

Step 3: Compute the value of $ f(2) $

Now substituting the simplified values back into the function: \[ f(2) = \frac{-3}{-16} = \frac{3}{16} \] Calculating the decimal value gives: \[ f(2) = 0.1875 \]

Final Answer

The value of $ f(2) $ is $\boxed{0.1875}$.

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