Inverses and Radical Functions and Relations

Operations

100

If f(x) = x + 2 and g(x) = 2x - 4, 

what is (f + g)(x)?

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

200

If f(x) = 2x and 

g(x) = -x - 4, 

what is (f - g)(x) ?

(f - g)(x) = 3x + 4

300

If f(x) = 6x + 1 and g(x) = 7x + 3

find (fg)(x).

(fg)(x)=42x^2+25x+3

400

If f(x) = 3x - 4 and g(x) = 6x - 5

Find (fog)(x)

(fog)(x) = 18x - 19

500

If f(x) = 3x - 1 and g(x) = 4x + 7

Find f(g(2))

f(g(2)) = (fog)(2) = 44

Inverses

100

f(x)={(3,2),(-2, 3)} 

Find

f^-1(x)

f^-1(x)={(2,3),(3,-2)}

200

If f = {(12,2), (-5,6 ), (6,-9), (-1,12)}, what is 

f^-1(x)?

 

f^-1(x)={(2,12),(6,-5),(-9,6), (12,-1)}

300

f(x)=10x+2. Find 

f^-1(x)

f^-1(x)=(x-2)/10

400

Find the Inverse of f(x) = (1/2)x + 3

f^-1(x)=2x-6

500

Find the Inverse of f(x) = (x/4) +24

f^-1(x)=4x-96

Square Root Functions

100

Find the domain and range

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

D={x|x>=-2}

R={y|y>=-3}

200

Find the domain and range

f(x)=3sqrt(x+4)

D={x|x>=-4}

R={y|y>=0}

300

Find the domain and range

h(x)=-2sqrt(x+2)+2

D={x|x>=-2}

R={y|y<=2}

400

Find domain and range and determine if the curve is solid/dashed and shade above/below

g(x)>=sqrt(x-3)+4

D={x|x>=3}

R={y|y>=4}

Solid, Shade Above

500

Find domain and range and determine if the curve is solid/dashed and shade above/below

g(x)<-2sqrt(x+5)-2

 

D={x|x> -5}

R={y|y<-2}

Dashed, Shade Below

Radical Expressions

100

Simplify 

root(3)(-81)

-3root(3)(-3)

200

Simplify 

sqrt(12)+sqrt(48)

6sqrt(3)

300

Simplify 

(3sqrt(5)-2sqrt(3))(2+sqrt(3))

6sqrt(5)+3sqrt(15)-4sqrt(3)-6

400

Simplify 

root(4)(625a^8b^(12))

5a^2|b|^3

500

Simplify 

root(3)(24a^6b^10)

2a^2b^3root(3)(3b)

Rational Exponents

100

Write using rational exponent

root(5)(b)

b^(1/5)

200

Evaluate 

32^(2/5)

   

4

300

Simplify 

x^(1/2)x^(2/3)

x^(7/6) or x(x^(1/6))

400

Simplify 

root(8)(81)/root(6)(3)

3^(1/3) or root(3)(3)

500

Simplify

(8^(1/6)-9^(1/4))/(sqrt(3)+sqrt(2)

2sqrt(6)-5