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Review (Answers)

1. (a) ()(x) = ; Domain = {x | x is a real number}
()(x) = -x + 2 ; Domain = {x | x is a real number}

(b) ()(x) = ; Domain =
()(x) = ; Domain = {x | x ³ -2}

(c) ()(x) = ; Domain =
()(x) = ; Domain =

2. (a) ()(-5) = 0
(b) ()(-1) = 4
(c) ()(4) = 6
(d) ()(-3) = Not possible because f(-3) = -6 and g(-6) is not defined.
(e) ()(-2) = 1
(f) ()(2) = 3

3. (a) ()(x) =
()(x) =
Since the composition of the functions gives x, the functions are inverses of each other.

(b) ()(x) =
()(x) =
Since the composition of the functions gives x, the functions are inverses of each other.

(c) ()(x) =
()(x) =
Since the composition ()(x) gives x only when x ³ 0, the
functions are NOT inverses of each other.

4.

(a) (i) The inverse is a function. It is:
(ii)

(b) (i) The inverse in NOT a function. It is:

(ii) Restricted function: x £ -2 gives

Restricted function: x ³ -2 gives

(c) (i) The inverse is NOT a function. It is:

(ii) Restricted function: x £ 3 gives

Restricted function: x ³ 3 gives