Hi, I am struggling with the attached HW problem. Any help is appreciated. Thanks. ### Mathematics Problem: Function PropertiesConsider the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 2x + 3 \).(i) **Show that \( f \) is one-to-one (1-1).**(ii) **Show that \( f \) is onto.**(iii) **Show that \( f(x) = x^2 \) from \( \mathbb{R} \) to \( \mathbb{R} \) is not one-to-one (1-1).**(iv) **Show that \( f(x) = x^2 \) from \( \mathbb{R} \) to \( \mathbb{R} \) is not onto.**This problem set asks to explore the properties of two different functions: \( f(x) = 2x + 3 \) and \( f(x) = x^2 \), specifically focusing on their injectivity (one-to-one nature) and surjectivity (onto nature).To approach these problems, one must:1. For one-to-one (injectivity), demonstrate that if \( f(x_1) = f(x_2) \) then \( x_1 = x_2 \).2. For onto (surjectivity), prove that for every \( y \) in the codomain, there exists an \( x \) in the domain such that \( f(x) = y \).Careful steps and logical arguments must be used to rigorously show these properties for each function in the problems provided.

Name: Hi, I am struggling with the attached HW problem. Any help is apprecia
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: Hi, I am struggling with the attached HW problem. Any help is appreciated. Thanks. ### Mathematics Problem: Function PropertiesConsider the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 2x + 3 \).(i) **Show that \( f \) is one-to-