Math Jeopardy

Xavier

100

Find f(4)

f(x)= x²+7x-18 / x²-8x+7

f(4)= -26/9

200

Write the expressions for (g*h)(x) and (g-h)(x) and evaluate (g + h)(4).

g(x)= 4x+1

h(x)= x+2

(g*h)(x)= 4x²+9x+2

(g-h)(x)= 3x-1

(g+h)(4)= 23

300

The functions r and s are defined as follows.

r(x)= 2x

s(x)= -x²-1

Find the value of r(s(-4)).

r(s(-4))= -34

400

Suppose that the functions h and f are defined as follows.

h(x)= x²-5

f(x)=x/3

Find the compositions h o h and f o f

Simplify your answers as much as possible.

(h o h)(x)= x⁴-10x+20

(f o f)(x)=x/9

500

Suppose H(x)= (x+5)²+3

Find two functions f and g such that (f o g)(x)=H(x)

f(x)= x²+3

g(x)= x+5

Emiliano

100

Get the domain of a fraction?

x²+9x-19

(-∞,∞)

200

g(9)

x⁴-x²+9x-98

6625

300

f(x)= x²+3                 g(x)=2x+1/2x+5

Find (f o g)

x=-5/2

400

f(x)=-x²+6

g(x)= x-9

Find f(g(4))=  

31

500

decompose the function

(10x-4)³

x³

10x'4

Gonzalo

100

r(x)=2x-1

s(x)=-x² -2

^{Find s(r(-2))=}    

^{s(r(-2))= -27}

200

Suppose

q(x)= -4x=4

r(x)=2x=1

(r o q)(-5)=

(q o r)(-5)=

(r o q)(-5)= 49

(q o r)(-5)= 40

300

g(x)= x+4/x-1

h(x)=4x-11

(g o h)= 4x-7/4x-12

(g o h)=4x-7/4x-12

400

suppose h(x)= (x-8)⁶ 

Find two functions f and g such that:(f o g) (x)=h(x)

f(x)= 

g(x)=

f(x)= x⁶

^g(x)=x-8

500

g(x)=5x

h(x)=3x-1

(g o h) (x)=

(g-h)(x)=

(g+h)(2)=

(g o h) (x)= 15x²-5x

(g-h)(x)= 2x+1

(g+h)(2)= 15

Miguel

100

decompose the function  correctly multiple answer

(7x-3)⁵

x⁵

^7x-3

200

decompose the function  correctly multiple answer

(2x+8)³

x³

^2x+8 

300

decompose the function  correctly multiple answer

(8x-1)⁴

x⁴

^8x-1

400

Find h(5)

x² +x-12/x² -4x-12 

h(5)=-18/7

500

Find the following 

u(x)=-4x+3

w(x)=-2x+1 

(w.u) and (u.w)

(w.u)(-2)=-21

(u.w)(-2)=-17

Pato

100

Supose P(x)= (x-12)²-2

Find two functions f and g such that (f o g)(x) = P(x) 

f = x²-2

g = x-12

200

How to get the domain of a fraction? x+2/x-15

All the real numbers except for 15

(-∞,15)U(15,∞)

300

A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S(in dollars) is given by the function S=0.88M=17.67 M is the number of miles driven 

The company also offers an option to insure the car against damage. The insurance charge I(in dollars) is given by the function I=0.15M+2.43

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M

Simplify your answer as much as possible.

C=1.03M+20.1

400

Find the following

p(x)=4x+9

a(x)=x²-14

(p o a)

(a o p)

(p o a)= 4x²-47

(a o p)= 16x²+72x+67

500

Find the composition g o h and specify its domain 

g(x)=x+5/x-2

h(x)= 2x-3

g o h= 2x+2/2x-5

domain= (-∞,5/2)U(5/2,∞)