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Cloud [144]
2 years ago
9

1. determine if the functions are inverse functions

Mathematics
1 answer:
kirill115 [55]2 years ago
5 0

Answer:

<u>Question 1</u>

The function f(x) = x + 6 is one-to-one, so it does have an inverse.

The inverse of +6 is -6, so f^{-1}(x)=x-6

Therefore, g(x) is the inverse of f(x).

<u>Question 2</u>

The function f(x) = -3x -9 is one-to-one, so it does have an inverse.

To find the inverse, replace f(x) with y:

\implies y = -3x -9

Rearrange the equation to make x the subject:

\implies y+9= -3x

\implies x=-\dfrac13(y+9)

\implies x=-\dfrac13y-3

Replace x with f^{-1}(x) and y with x:

\implies f^{-1}(x)=-\dfrac13x-3

Therefore, g(x) is the inverse of f(x).

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