Question

how do I combine this function?
if f(x)=x^2+5x-6 and g(x)=x-1, find (f.g)(x) and (f/g)(x)

Answer 1

For the second part, (f/g)(x), just use long or synthetic division. It is saying to divide f(x) by g(x). You should get (x + 6) as you answer.
The first part of the problem is unclear. Is it saying f(g(x)),which means f of g of x, or is it saying f(x) times g(x)?

Answer 2

thanks for your reply! im not sure but thats just what it looked like. the dot was in the middle though (f (with dot in middle) g)(x)

Answer 3

Well if it was (fog) which means the same thing as f(g(x)),
Then just sub the function g(x) wherever you see an 'x' in the f(x) function.
You should get:
x^2 +3x -10
Or in factored form... (x+5)(x-2)

2. If it was (f*g)(x), meaning f times g,
Then multiply the two functions and obtain a polynomial to the 3rd degree:
(x^2 +5x - 6)(x-1)
= x^3 + 6x^2 - 11x +6
Or in factored form... (x-1)(x-1)(x+6)

Answer 4

thank you for your help!!