Composition of Functions

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

• 10x-1

• 10x-5

• 5x²-1

• 5x²-5

Tags

CCSS.HSF-BF.A.1C

If  $f\left(x\right)=\frac{1}{x}$   and  $g\left(x\right)=3x+2$   find  $\left(g\circ f\right)\left(x\right)$  

•  $\frac{1}{3x}+2$ 

•  $3x+2$  

•  $\frac{3}{x}+2$  

•  $\frac{1}{3x+2}$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

If  $f\left(x\right)=x^2$   and  $g\left(x\right)=\sqrt{x}$   find  $f\left(f\left(x\right)\right)$  

•  $x^4$  

•  $2x^2$  

•  $2x^4$  

•  $x^3$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

If  $f\left(x\right)=2x$   and  $g\left(x\right)=2x^2-1$   find  $g\left(f\left(x\right)\right)$  

•  $4x^2-1$  

•  $4x^2-2$  

•  $8x^2-1$  

•  $16x^2-1$  

Tags

CCSS.HSF-BF.A.1C

If  $f\left(x\right)=2x$   and  $g\left(x\right)=2x^2-1$   find  $f\left(g\left(3\right)\right)$  

• 34

• 71

• 35

• 142

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Determine which two functions are composed so that  $f\left(g\left(x\right)\right)=h\left(x\right)$ , where  $h\left(x\right)=\left(x-3\right)^2-5.$ 

• f(x) = x - 3; g(x) = x² - 5

• f(x) = (x - 3)²; g(x) = x - 5

• f(x) = x - 7; g(x) = (x - 3)²+2

• f(x) = x²; g(x) = (x - 3) - 5

If f(x) = ∛(x), g(x) = 2x - 5, h(x) = 2x² and j(x) = |x + 3|, which ones were composed and in what order to create the following function?
C(x) =  2(|x+ 3|)^⅔

• j(h(x))
• h(f(g(x)))
• h(j(x))
• h(f(j(x)))

When solving f(g(x)) you work in what order?

• Left to right
• Alphabetical
• INSIDE then OUT
• It doesn't matter what you solve first, just pick your favorite letter.

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

Tags

CCSS.HSF-BF.A.1C

Given f and g in the graph,
what is  $\left(f\circ g\right)\left(-1\right)?$ 

• 1

• 4

• -1

• 6