Function Composition & Inverses Review Game

Thursday Throwback

100

What is the domain of the following function? 

f(x)= x² -1

All Real Numbers!

200

Describe the End Behavior of the following function: 

f(x)= -3x³+4

As x approaches negative infinity, f(x) approaches positive infinity. 

As x approaches positive infinity, f(x) approaches negative infinity. 

300

Determine the intervals for which the function f(x)=x³ is increasing and/or decreasing. 

Increasing: (-infinity, infinity)

Decreasing: None

400

Identify both the absolute and relative extrema of the following function: 

f(x)-2x³+4x

Absolute Max: None 

Absolute Min: None 

Relative Max: (0.816, 2.177)

Relative Min: (-0.816, -2.177)

500

Prove whether the following function is even, odd, neither, or both:

f(x)= x³+2x²

NEITHER 

f(-x)= -x³+2x²

-f(x)= -x³-2x²

Composition City

100

f(x)= x

Find f(4)

f(4)=4

200

f(x)=x³-14x+2

Find f(2)

f(2)= -18

300

f(x)= x , g(x)= x²-1

Find f(g(3))

f(g(3))= 8

400

a(x)= e^x    b(x)= x²

Find b(a(2))

b(a(2))= e⁴

500

f(x)= x+1    g(x)= x³     h(x)= 14x

Find f(g(h(.5)))

f(g(h(.5)))= 344

Funky Compositions

100

f(x)= x     g(x)= 12x-2

Find f(g(x))

f(g(x))= 12x-2

200

f(x)= x²-x    g(x)= 2

Find f(g(x))

f(g(x))= 2

300

f(x)= x³     g(x)= x+3

Find f(g(x))

f(g(x))= (x+3)³ = x³+9x²+27x+27

400

f(x)= x²    g(x)= x-4    h(x)= e^x

Find g(h(f(x)))

g(h(f(x)))= _ex² -4

500

a(x)= ln(x)   b(x)= e^2x+3    c(x)= x⁴

Find b(a(c(x)))

b(a(c(x)))= x⁸+e³

Name That Inverse!

100

Determine the inverse of f(x)= x+4

f ^-1(x)= x-4

200

Determine the Inverse of y= x²+1

f ^-1(x)= rad(x-1)

300

Determine the Inverse of the following function AND state its domain: 

f(x)= 4x-3

f ^-1(x)= (x+3)/4 

Domain: All Real Numbers

400

Determine the Inverse of the following function AND state its Domain: 

y= x²-4

f ^-1(x)= rad(x+4)

Domain: [-4, Infinity)

500

Determine the Inverse of the following function AND state its Domain: 

f(x)= (x+7)/(x-2)

f ^-1(x)= (2x+7)/(x-1)

Domain: (-Infinity, 1), (1, Infinity)

Show Me The Inverses!

100

In order to prove two functions are Inverses of one another, what must you show?

f(f ^-1(x)) = f ^-1(f(x)) = x

200

Prove whether or not the following functions are Inverses: 

f(x)= x²     g(x)= rad(x)

They are, in fact, Inverses:

f(g(x))= x

g(f(x))= x

300

Prove whether or not the following functions are Inverses: 

f(x)= 2x-1    g(x)= (x-1)/2

They are not Inverses. 

f(g(x))= x-2

g(f(x))= x-1

400

Prove whether the following functions are Inverses: 

f(x)= (x-12)/4     g(x)= 4x+12

They are, in fact, Inverses: 

f(g(x))= x

g(f(x))= x

500

Prove whether or not the following functions are Inverses: 

f(x)= (x+2)/(x-2)     g(x)= (2x+2)/(x-1)

They are, in fact, Inverses:

f(g(x)) = g(f(x)) = x