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Answer:
Arc
Step-by-step explanation:
The inverse of f does NOT exist. The reason why is because the function fails the horizontal line test. Recall that the horizontal line test is a test where you try to see if you can pass a single horizontal line through more than one point on the function curve. If you can get the horizontal line to pass through more than one point, then it fails the test. It's very similar to the vertical line test.
Answer:







Step-by-step explanation:
Required
Simplify
Solving (1):

Factorize the numerator and the denominator

Factor out x+2 at the numerator

Express x^2 - 9 as difference of two squares


Expand the denominator

Factorize


Cancel out same factors

Hence:

Solving (2):

Expand the numerator and factorize the denominator

Factorize the numerator

Factor out x - 2

Cancel out x - 2

Hence:

Solving (3):

Express x^2 - 9 as difference of two squares

Factorize all:

Cancel out x + 3 and 3 + x


Express
as 



Hence:

Solving (4):

Expand x^2 - 6x + 9 and factorize 5x - 15

Factorize


Cancel out x - 3

Change / to *

Express
as 



Hence:

Solving (5):

Factorize the numerator and expand the denominator

Factor out x - 1 at the numerator and factorize the denominator

Express x^2 - 1 as difference of two squares and factor out x - 1 at the denominator


Hence:

Solving (6):

Factorize:

Divide by 3x

Hence:

Solving (7):

Change / to *

Expand

Factorize


Cancel out x - 2 and x - 1

Cancel out x



Hence:
