Questions: f(x)=2(x-3)^2-1 f(x)=2 (x^2-2 x 3+3^2)-1 f(x)=2 x^2

Transcript text: f(x)=2(x-3)^{2}-1 f(x)=2 \cdot\left(x^{2}-2 \cdot x \cdot 3+3^{2}\right)-1 f(x)=2 x^{2}

Solution

To solve the given function \( f(x) = 2(x-3)^2 - 1 \), we need to expand and simplify the expression. The steps involve:

Step 1: Define the Function

We start with the function defined as: \[ f(x) = 2(x-3)^2 - 1 \]

Step 2: Substitute \( x = 5 \)

Next, we substitute \( x = 5 \) into the function: \[ f(5) = 2(5-3)^2 - 1 \]

Step 3: Calculate the Squared Term

Calculating the squared term: \[ 5 - 3 = 2 \quad \Rightarrow \quad (5-3)^2 = 2^2 = 4 \]

Step 4: Multiply by 2 and Subtract 1

Now, we multiply by 2 and subtract 1: \[ f(5) = 2 \cdot 4 - 1 = 8 - 1 = 7 \]

Thus, the value of the function at \( x = 5 \) is: \[ \boxed{7} \]

Was this solution helpful?

Unhelpful

Helpful

Thank you for your feedback.

Copied!