Distributive Property?

1. Mar 11, 2013

TheFabricator

Hi All,

I am teaching my self algebra using khan academy and Ive come across a problem I cant figure out. I am trying to solve composite functions and I cant figure out why a Plus sign is added to the equation, Could I be missing something that I am suppose to distrubute?

The functions is:

g(f(−1))=?

h(x)=4x+2

g(n)=n^3+2n^2−7n+5+f(n)

f(t)=3t−h(t)

f(−1)=−1

g(−1)=(−1)^3+2(−1)^2 + (−7)(−1)+5+f(−1)

where does this............Δ Plus sign come from?

2. Mar 11, 2013

Staff: Mentor

This can be written as
g(n)=n^3+2n^2+(−7)n+5+f(n)

Alternatively, you can drop your plus sign and write
g(−1)=(−1)^3+2(−1)^2 −7(−1)+5+f(−1)

3. Mar 11, 2013

TheFabricator

Ok thank you, But why can it be written that way? How does the plus sign get there from the equation. Can you expand on that or point me in the right direction on how to find out.

4. Mar 11, 2013

Staff: Mentor

There is no difference between substrating a number and adding a negative number:
$$a - b = a + (-b) = -b + a$$

5. Mar 11, 2013

TheFabricator

Ah ok I understand now, Thank you