Question

Fill in each blank so that the resulting statement is true. If f(x)=x²-3x+2 , it is possible to find f(x+4) by replacing each occurence of_ by_ If f(x)=x²-3x+2 , it is possible to find f(x+4) by replacing each occurence of by □

Answer 1

To find f(x+4), replace x with (x+4) in the function f(x) = x² - 3x + 2, expand, and simplify to get the new expression f(x+4) = x² + 5x + 6.

Step-by-step explanation:

To find f(x+4) given f(x) = x² - 3x + 2, you need to replace the x in f(x) with x+4. This process is commonly referred to as function composition, specifically finding f of a transformed argument. Here are the steps:

1. Start with the original function: f(x) = x² - 3x + 2.
2. Replace every occurrence of x with (x+4): f(x+4) = (x+4)² - 3(x+4) + 2.
3. Simplify the equation by expanding the square and distributing the -3: f(x+4) = x² + 8x + 16 - 3x - 12 + 2.
4. Combine like terms: f(x+4) = x² + 5x + 6.

This completion of the square shows that the replacement process results in a new quadratic expression representing f(x+4).