Function Operations and Composition Flashcards

Question 1

What is the sum of two functions $(f+g)(x)$?

Accepted Answer

$$(f+g)(x)=f(x)+g(x)$$ Defined for all $x$ in $
	ext{dom}(f)\cap	ext{dom}(g)$.

Question 2

Find the domain of $\left(\frac{f}{g}\right)(x)$ if $f(x)=\sqrt{x-1}$ and $g(x)=x-3$.

Accepted Answer

Need $x-1\ge 0$ and $x-3
eq 0$, so $x\ge 1$ with $x
eq 3$. Domain: $[1,3)\cup(3,\infty)$.

Question 3

What is the horizontal line test and what does it tell you?

Accepted Answer

A graph passes the horizontal line test if every horizontal line intersects it at most once; this means the function is one-to-one and therefore has an inverse function (on that domain).

Function Operations and Composition Flashcards

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