Function Operations and Domain

• 42

• 30

• 26

• 43

 What is the domain of $f\left(x\right)=\frac{3}{2}x+9$ 

•  $\left(-\infty,\infty\right)$  
  

•  $\left[-6,\infty\right)$  

•  $\left(-\infty,-6\right]$  

•  $\left(-\infty,-6\right)U\left(-6,\infty\right)$  

If  $f\left(x\right)=-3\sqrt{x+2}$   and  $g\left(x\right)=4x+5$  what is  $f\left(7\right)-g\left(3\right)$  ?

• -9

• 8

• -26

• 17

Tags

CCSS.HSF.IF.A.2

Use the graph to find x when g(x)=5.

• -3

• 3

• 5

• -5

Tags

CCSS.HSF.IF.A.2

If  $f\left(x\right)=x^2+4x+12$  then for what values of x is  $f\left(x\right)=24$  ?

• x  =6 or -2

• x = -6 or 2

• x = 3 or 4

• x = -3 or -4

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

If  $f\left(x\right)=2x^3+8x^2-10x$ and  $g\left(x\right)=x+8$  find the domain of  $\frac{f\left(x\right)}{g\left(x\right)}$  

•  $\left(-\infty,\infty\right)$  
  

•   $\left(-\infty,-8\right)U\left(-8,\infty\right)$  

•   $\left(-\infty,0\right)U\left(0,1\right)U\left(1,\ -5\right)U\left(-5,\infty\right)$  

•   $\left(-\infty,0\right)U\left(0,\ 1\right)U\left(1,\ -5\right)U\left(-5,\ -8\right)U\left(-8,\infty\right)$  

g(x) = -3x+7

h(x) = -x-10

Find g(x)/h(x) and the domain restriction

• $\frac{\left(-3x+7\right)}{-x-10};\ \ domain\left(-\infty,\frac{7}{3}\right)U\left(\frac{7}{3},\infty\right)$

• $\frac{\left(-3x+7\right)}{-x-10};\ domain\left(-\infty,-\frac{7}{3}\right)U\left(-\frac{7}{3},\infty\right)$
  

• $\frac{\left(-3x+7\right)}{-x-10};domain\left(\infty,10\right)U\left(10,\infty\right)$
  

• $\frac{\left(-3x+7\right)}{-x-10};domain\left(-\infty,-10\right)U\left(-10,\infty\right)$

True or false: It is always true that  $\left(f+g\right)\left(x\right)\ =\ \left(g+f\right)\left(x\right)$ . 

• True

• False

If  $f\left(x\right)\ =\ -x^2+3$  and  $g\left(x\right)\ =\ x^3+2x^2-2$ , then  $\left(f-g\right)\left(x\right)\ =\ ...$   

•  $x^3+x^2+1$  

•  $x^3+3x^2-5$  

•  $-x^3-3x^2+5$  

•  $0$