Determine whether these functions are invertible. Find inverses of the invertible functions.

(a) $ f(x) = x - 2 $.

(b) $ f(x) = x^{2} $, where $ x \in \mathbb{R} $.

(c) $ f(x) = x^{2} $, where $ x \in (2, 5) $.

(d) $ f(x) = x^{3} $.

Question

Determine whether these functions are invertible. Find inverses of the invertible functions.

(a) $ f(x) = x - 2 $.

(b) $ f(x) = x^{2} $, where $ x \in \mathbb{R} $.

(c) $ f(x) = x^{2} $, where $ x \in (2, 5) $.

(d) $ f(x) = x^{3} $.

Anonymous · Answer

b) is not invertible, while the others are. a) The inverse is x+2 c) The inverse is x ​ d) The inverse is 3 x ​

Determine whether these functions are invertible. Find inverses of the invertible functions.

(a) \( f(x) = x - 2 \).

(b) \( f(x) = x^{2} \), where \( x \in \mathbb{R} \).

(c) \( f(x) = x^{2} \), where \( x \in (2, 5) \).

(d) \( f(x) = x^{3} \).