Solving Composite Functions with Distributive Property

[TheFabricator]

Hi All,

I am teaching my self algebra using khan academy and I've come across a problem I can't figure out. I am trying to solve composite functions and I can't 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?

 

[mfb]

g(n)=n^3+2n^2−7n+5+f(n)

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)

 

[TheFabricator]

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)

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.

 

[DrClaude]

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.

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

 

[TheFabricator]

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

Ah ok I understand now, Thank you