M13: Functions & Inverses

Question 1

Use inverse operations to find the inverse

ƒ(x) = 5x − 1

Answer 1

Answer: (x+1)/5

Steps:
x=5y-1
Switch Sides:
5y-1=x
Add one to each side:
5y-1+1=x+1
Simplify:
5y=x+1
Divide by 5:
5y/5=x/5+1/5
Simplify:
y=(x+1)/5

Question 2

Use inverse operations to find the inverse of

y = 8x^3

Answer 2

Answer: (3√ x) / 2

Steps:
x=8y^3
Switch sides:
8y^3=x
Divide both sides by 8:
(8y^3)/8=x/8
Simplify:
y^3=x/8
For x^n = f(a), n is odd, the solution is x=n√ f(a):
y=3√ (x/8)
Simplify:
y=(3√ x) / 2

Question 3

Functions and their inverses appear to be reflections across which line?

Answer 3

Answer: The y-axis

Question 4

Are all inverses of functions, functions?

Answer 4

Answer: Yes they are Functions

Question 5

How are the domain and range of a relation related to the domain and range of its inverse?

Answer 5

Answer: The relationships is that the domain of the function becomes the range of its inverse and the range of the function becomes the domain of it’s inverse.

Question 6

Use inverse operations to find the inverse f(x) = 2x

Answer 6

The inverse is ƒ -1 (x) = x /2 .

Question 7

How does the degree of a polynomial affect its end behavior?

Answer 7

The degree of a polynomial is the assets of polynomial because its solution at the end depending on it if it 2 than number of solution is 2 and so on

Question 8

Is the function ƒ (x) = x^3 an odd or even function?

Answer 8

Answer: Odd function

Question 9

Use inverse operations to find the inverse f(x) = 5x − 1

Answer 9

Answer: y={x+1}/{5}

Question 10

When you take the cube root of a number or variable, do you have to consider both positive and negative cases?

Answer 10

Answer: No because a real number only has one cube root.
Cube root of a positive number is positive.
Cube root of a negative number is negative.