Can I have these two with steps please?

Question

1) Find (f+g)(1) when f(x)=x+6 and g(x)=x-3

 

2) For (x)=x^2-4 and g(x)=2x+3, what is the domain of f/g?

Answer 1

Ralph, (f + g)(1) is shorthand for f(1) + g(1).

 

(f + g)(1) = 1 + 6 + 1 - 3 = 5

 

If you are diving the two, then the only thing we can't do is have the denominator = 0.

 

2x + 3 = 0

2x = -3

x = -3/2

 

So, the domain is all real numbers except -3/2.