Ch. 6 Review

Ch. 6.1

100

Find (f+g)(x)

f(x)=2x

g(x)=-4x+5

-2x+5

200

Find

(f@g)(x)

f={(1,2),(3,4),(5,6)}

g={(0,1),(2,3),(4,5)}

{(0,2),(2,4),(4,6)}

300

Find

(f/g)(x)

f(x)=3x and g(x)=-2x+6

(3x)/(-2x+6), xne3

400

Find

[f@g](x)

f(x)=x+4 and g(x)=x^2+3x-10

x^2+3x-6

500

Find

[g@f](x)

f(x)=2x^2 and g(x)=8x^2+3x

32x^4+6x^2

Ch. 6.2

100

Find the inverse of the relation.

{(-9,10),(1,-3),(8,-5)}

{(10,-9),(-3,-1),(-5,8)}

200

Find the inverse of the function.

f(x)=-2x+1

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

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

300

Find the inverse of the function.

h(x)=x^2-3

h^-1(x)=+-sqrt(x+3)

400

Determine whether the pair of functions are inverse functions. Yes or No.

f(x)=1/3x+3 and g(x)=-3x+9

Yes

500

Determine whether the pair of functions are inverse functions. Yes or No.

f(x)=4x^2 and g(x)=1/2sqrt x

Yes

Ch. 6.3

100

Identify the domain and the range of the function.

f(x)=sqrt(4x)

D={x|x>=0 and R=f(x)|f(x)>=0}

200

Identify the domain and the range of the function.

f(x)=sqrt(x+8)-2

D={x|x>=-8} and R={f(x)|f(x)>=-2}

300

State the Vertical and Horizontal Translation of the function.

f(x)=sqrtx-2

Vertical translation, 2 units down.

No Horizontal translation.

400

State the Vertical and Horizontal Translation of the function.

f(x)=sqrt(x+3)+2

Vertical translation, 2 units up

Horizontal translation, 3 units left

500

State the Vertical and Horizontal translation of the function.

y=sqrt(4x-12)+8

Vertical Translation, 8 units up

Horizontal Translation, 3 units to the right

Ch. 6.4

100

Simplify

+-sqrt(16x^8)

+-4x^4

200

Simplify

-sqrt((q^3+5)^4

-(q^3+5)^2

300

Simplify

root5(243a^10b^15)

3a^2b^3

400

Simplify

root8(x^16y^8)

x^2|y|

500

Simplify

root4(256(5x-2)^12)

4|(5x-2)^3|

Ch. 6.5

100

Simplify

sqrt(25a^4b^9)

5a^2b^4sqrtb

200

Simplify

sqrt(y^8/x^7

(y^4sqrtx)/x^4

300

Simplify

3sqrt(45)-5sqrt(80)+4sqrt(20)

-3sqrt5

400

Simplify

(2sqrt3+3sqrt5)(3-sqrt3)

6sqrt3-6+9sqrt5-3sqrt15

500

Simplify

(9-2sqrt3)/(sqrt3+6)

(20-7sqrt3)/(11

Ch. 6.6

100

Write 

a^(2/7)

in radical form.

root7(a^2)

200

Evaluate the expression

32^(2/5)

4

300

Simplify the expression.

y^(1/7)cdot y^(4/7)

y^(5/7)

400

Simplify the expression.

root6(16)/(root3(2)

2^(1/3) or root3(2)

500

Simplify the expression.

(y^(1/2)+1)/(y^(1/2)-1)

(y+2y^(1/2)+1)/(y-1)

Ch. 6.7

100

Solve the equation.

2sqrt(3x+4)+1=15

x=15

200

Solve the equation.

(3y+1)^(1/3)+5=0

-42

300

Solve the equation.

sqrt(x-12)=2-sqrtx

no solution

400

Solve

sqrt(3x-6)+4<=7

{x|2<=x<=5}

500

Solve

sqrt(b-7)+6<=12

{b|7<=b<=43}