Inverse and Radical Functions

Operations with Functions

100

Given f(x)=3x² + 7x and g(x)=2x²-x-1, find the function, (f +g)(x).

5x²+6x-1

200

Given f(x)=3x²-2x+1 and g(x)=x-4, find the function, (f x g)(x).

3x³-14x²+9x-4

300

If f(x)=-x+1, g(x)=4x+2, and h(x)=x²-1, find (3f+2h)(0)

1

Composition of Functions

100

Given f(x)=-x+8 and g(x)=2x²+x, find the value of [f x g](2).

g=10 

f=-2

200

Given f(x)=-x+8 and g(x)=2x²+x, find the value of [g x f](2).

f=6 

g=78

300

Find [f x g](x) and [g x f](x), state the domain and range.

[f x g](x)={(7,-1),(-1,7),(4,4),(8,6)} 

[g x f](x)={(9,9),(7,0),(0,7)}

Inverse Functions and Relation

100

What is the inverse of f(x)=3x+2?

f^-1(x)=(x-2)/3

200

Find the inverse of f(x)=(x-3)/5

f^-1(x)=5x+3

300

Determine whether f(x)=(3/4x)-6 is an inverse. 

Yes

Square Root and Cube Root Functions

100

Find the domain and range of f(x)=√(x-2)

Domain:[2, Infinity) 

Range:[0,Infinity)

200

Find the domain and range of f(x)=√(x+6)+2

Domain:[-6,Infinity) 

Range:[2,Infinity)

300

Describe the key characteristics of f(x)=³√(x+4)

Domain:(-Infinity,+Infinity) 

Range:(-Infinity,+Infinity) 

End Behavior:(as x approaches -Infinity, f(x) approaches -Infinity), (as x approaches +Infinity, f(x) approaches +Infinity) 

Inflection Point:(-4,0) 

Solving Radical Equations

100

Solve, √(x-12)=2

x=16

200

Solve, (3y+1)^1/2+5=0

y=-42

300

Solve, √(4x-4)-2<4

Y=[1,10)