Composition of Functions, verify something for me.
Let $f(x) = 9 – x^2, g(x) = 3 – x$. Find $(f – g)(x)$.

My work:
$f(x) = 9 – x^2, g(x) = 3 – x$
$(9 - x^2) - (3 - x)$
$9 - x^2 - 3 + x$

Apply some properties:
$-x^2 + x + 6$

I am certain I did do everything correctly, however Composition of Functions is something I studied a long time ago. I would like verification as my teacher did not give me the marks for this question.

Question

Composition of Functions, verify something for me. 
Let $f(x) = 9 – x^2, g(x) = 3 – x$. Find $(f – g)(x)$.

My work:
$f(x) = 9 – x^2, g(x) = 3 – x$
$(9 - x^2) - (3 - x)$
$9 - x^2 - 3 + x$

Apply some properties:
$-x^2 + x + 6$

I am certain I did do everything correctly, however Composition of Functions is something I studied a long time ago. I would like verification as my teacher did not give me the marks for this question.

anonymous · Answer

This isn't a composite function, but your answer is right.
$$(f-g)(x)=f(x)-g(x)$$
Your work is correct.

opcode · Answer

Supposedly my teacher said it was, odd. Mind telling me what it is actually?

anonymous · Answer

Just function subtraction. One of the fundamental operations that can be done on the set of functions. The others are addition (of which subtraction is a special case), multiplication/division, and composition.

opcode · Answer

I see, thank you. :-)