Combining Functions and Domain

Perform (g - f)(x) given  $g\left(x\right)=-2x-1$  and  $f\left(x\right)=3x+4$  

•  $5x+5$  

•  $-5x-5$  

•  $-x^2+2x-4$  

•  $-5x+5$  

Perform $\left(h\cdot g\right)\left(x\right)$  given  $h\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-4$  

•  $2x^3-5x^2-8x+20$  

•  $-2x^3-3x^2+9x$  

•  $-4x^2+8x$  

•  $-2x^3-5x^2+8x+20$  

 $f\left(x\right)=x^2+1$  and  $g\left(x\right)=x+1$  Which of the following best represents  $f\left(g\left(x\right)\right)$  ?

•  $x^2+2$  

•  $x^2+2x+2$  

•  $x^2+3$  

•  $x^2+4x+4$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What kind of number does not produce a real number if under an even root?

• a fraction

• whole number

• negative number

• zero

Find the domain of

 $f\left(x\right)=\sqrt{x+3}$  

•  $-3\le x<\infty$  

•  $-\infty<x\le-3$  

•  $3\le x<\infty$  

• All Real Numbers

What number CANNOT be in the denominator of a fraction?

• a negative number

• 0

• 1

• any whole number

Find the domain of

 $f\left(x\right)=\frac{x+1}{x-3}$  

•  $-\infty<x<3\ and\ 3<x<\infty$  

•  $-\infty<x<-1\ and\ -1<x<\infty$  

•  $3<x<\infty$  

•  $-\infty<x<-1\ and\ -1<x<3\ and\ 3<x<\infty$  

What is the domain of

 $f\left(x\right)=\frac{2}{x-4}$  

•  $-2<x<\infty$  

•  $4<x<\infty$  

•  $-\infty<x<\infty$  

•  $-\infty<x<4\ and\ 4<x<\infty$  

Find the domain of the function

 $f\left(x\right)=\sqrt{x-5}$  

•  $5<x<\infty$  

•  $5\le x<\infty$  

• all real numbers

•  $-\infty<x<5\ and\ 5<x<\infty$  

Find the domain of  $f\left(x\right)=\frac{x-3}{\sqrt{3-x}}$  

•  $-\infty<x\le3$  

•  $3<x<\infty$  

•  $-\infty<x<3\ and\ 3<x<\infty$  

•  $-\infty<x<-3\ and\ -3<x<3\ and\ 3<x<\infty$