Question

For the given function f(x)=x²-5x-7, find f(x+3).

Answer 1

To find f(x+3) for the function f(x)=x²-5x-7, replace x with (x+3) and simplify to get f(x+3)=x²+x-13.

Step-by-step explanation:

To find f(x+3) for the given function f(x) = x² - 5x - 7, you'll want to replace every x in the function with (x+3). Here's how you do it step by step:

1. Start with the original function: f(x) = x² - 5x - 7.
2. Replace every x with (x+3): f(x+3) = (x+3)² - 5(x+3) - 7.
3. Expand the squared term: (x+3)² = x² + 6x + 9.
4. Distribute the -5 across (x+3): -5(x+3) = -5x - 15.
5. Combine all terms: f(x+3) = x² + 6x + 9 - 5x - 15 - 7.
6. Simplify the expression: f(x+3) = x² + 1x - 13.

So, f(x+3) = x² + x - 13 is the function for f evaluated at x+3.