Questions: Following the steps from the question in this video what is f(x+h) for the function f(x)=x^2-x-3 x^2+h^2-x+h-3 x^2+2xh+h^2-x-h-3 x^2+2xh+h^2-x+h-3 None of the above

Following the steps from the question in this video what is f(x+h) for the function f(x)=x^2-x-3

x^2+h^2-x+h-3

x^2+2xh+h^2-x-h-3

x^2+2xh+h^2-x+h-3

None of the above

Transcript text: Following the steps from the question in this video what is $f(x+h)$ for the function $f(x)=x^{2}-x-3$ $x^{2}+h^{2}-x+h-3$ $x^{2}+2 x h+h^{2}-x-h-3$ $x^{2}+2 x h+h^{2}-x+h-3$ None of the above SUBMIT

Solution

Solution Steps

To find $ f(x+h) $ for the function $ f(x) = x^2 - x - 3 $, we need to substitute $ x+h $ into the function in place of $ x $.

Step 1: Define the Function $ f(x) $

The given function is: \[ f(x) = x^2 - x - 3 \]

Step 2: Substitute $ x + h $ into the Function

To find $ f(x + h) $, substitute $ x + h $ into the function: \[ f(x + h) = (x + h)^2 - (x + h) - 3 \]

Step 3: Expand the Expression

Expand the expression: \[ f(x + h) = (x + h)^2 - (x + h) - 3 \] \[ = x^2 + 2xh + h^2 - x - h - 3 \]

Step 4: Simplify the Expression

Combine like terms: \[ f(x + h) = x^2 + 2xh + h^2 - x - h - 3 \]

Final Answer

$\boxed{f(x + h) = x^2 + 2xh + h^2 - x - h - 3}$

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