Help with functions

Question

I'm doing a problem with functions and it's asking me to find f(a+7) and simplify. The original problem is f(x)=x+5/(x-8)^2...I plugged in f(a+7) and came up with this f(a+7)=(a+7)+5/((a+7)-8)^2. I'm wondering do I cancel out (a+7) in the numerator and denominator, then solve? I just need some help please.

Answer 1

You did the correct substitution. Now simplify the numerator and denominator and see what you end up with. That should be all you need to do since the question is not asking you to solve for a.

Answer 2

Hi April,

 

The (a+7) expressions that appear in the numerator and denominator are not FACTORS, so cannot be cancelled.

 

If you had something that looked like this:

 

[(a+7)(2a-5)]/[2(a+7)], then indeed the (a+7) expressions could be cancelled, resulting in (2a-5)/2.

 

For your problem the numerator simplifies to (a+12).

The denominator simplifies to (a-1)². At that point there are no common factors between numerator and denominator. You could choose to expand the denominator to (a²-2a+1).