Solving Radical Eqs, Functions, Inverses

Process

100

What is the first step to solving a radical equation?

Isolate the radical to one side, if necessary.

200

What is the formula for adding / subtracting two functions? Write the formula

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

(f-g)(x) = f(x) - g(x)  

300

What are the 3 steps to solve an inverse function?

1. Let f(x)=y

2. Switch x and y 

3. Solve for y

400

How do you determine the domain of the division of two functions, (f/g)(x)?

Set the denominator to zero and solve for the values of x that make the denominator undefined.

500

What two checks must you perform to evaluate if two functions are inverses of each other? Write the formulas.

f( g(x) ) = x 

g ( f(x) ) = x 

Definitions

100

What is the domain of the sum, difference or multiplication of two functions?

All Real Numbers

200

What is a radical equation? 

An equation that contains a variable within a radical.

300

What is an extraneous solution? How do you check for it?

An extraneous solution is not a solution to the original equation. You check by plugging in the value of x and verifying the equation. 

400

When performing the horizontal line test, a function is _________ if the line crosses _____. A function is _________, if the line crosses ________. 

Invertible, once.

Non-invertible, more than once. 

500

What are the 3 characteristics of all inverse functions?

1. The ______ and ______ switch.

2. The ______ and ______ switch.

3. F inverse is a reflection across the line ________.

Solving Radical Eq

100

(x-14)^1/3 = -2

x = 6

200

4(x)^1/2 + 3 = 23

x = 25

300

(4x-4)^1/2 = (x+11)^1/2

x = 5 

400

(4x-1)^1/3 = (6x+5)^1/3

x = -1

500

(2x²+8)^1/4 = x

x = 2

Function Operations

100

f(x) = 5x² + 3 ; 

g(x) = 6x² - 7. Find (f+g)(x) 

(f+g)(x)= 11x² - 4

200

If (f-g)(x) = x³ - 2x² + 8. What is (f-g)(1)? 

(f-g)(1)= 7 

300

f(x) = 10x² + 5x - 1 ; 

g(x) = 2x. Find fg(x)

fg(x) = 20x³ + 10x² - 2x

400

What is the domain of 

(f/g)(x) = 5x + 7 / x²

Domain: All real numbers, x cannot be zero

500

f(x) = 15x² - 5x  ; 

g(x) = 5x(x-1). Find (f/g)(x)

(f/g)(x) = 3x - 1 / x - 1 

Inverse Functions

100

Find the inverse of 

f(x) = 2x + 1 

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

200

Find the inverse of 

f(x) = 1/4 (x) + 3

f^-1(x) = 4(x - 3)

300

Determine if f(x) = x⁴- 5x³ + 4x - 9 is invertible. If so, find the inverse. 

Function is even, graph is non-invertible.

400

Find the inverse of

f(x) = 4x³ - 6

f^-1(x) = (x+6 / 4)^1/3

500

Determine whether the functions are inverses of each other. f(x) = 6x - 1 ; g(x) = (x+1)/6

They are :)