1.5.5 State whether \( v(x) \) is a function or not, and motivate your answer. 1.5.6 Write down the conditions that will make \( v \) a function. 1.5.7 Determine all values of: 1.5.7.1 \( y \) for which \( w(x)<0 \) 1.5.7.2 \( x \) for which \( w(x)<-\frac{7}{10} \) 1.5 .8 If a function is as determined in 2.2 , write down the equation(8) of \( v^{-1}(x) \). 1.5.9 If \( h(x)=w(x)-\sqrt{x} \) where the rango of \( \sqrt{x} \) is \( (0 ; \infty) \), calculate the range of \( h(1) \) (1)

To address the questions, we need to analyze the function \( v(x) \) and the function \( w(x) \). Let's go through each part step by step. ### 1.5.5 State whether \( v(x) \) is a function or not, and motivate your answer. A relation \( v(x) \) is considered a function if for every input \( x \), there is exactly one output \( v(x) \). To determine if \( v(x) \) is a function, we need to check if any input \( x \) corresponds to multiple outputs. **Motivation:** - If \( v(x) \) passes the vertical line test (i.e., any vertical line intersects the graph of \( v(x) \) at most once), then \( v(x) \) is a function. - If there exists at least one \( x \) such that \( v(x_1) = v(x_2) \) for \( x_1 \neq x_2 \), then \( v(x) \) is not a function. ### 1.5.6 Write down the conditions that will make \( v \) a function. For \( v(x) \) to be a function, the following conditions must be satisfied: 1. Each input \( x \) must map to exactly one output \( v(x) \). 2. The relation must not have any \( x \) values that produce multiple \( v(x) \) values. 3. The domain of \( v \) must be clearly defined. ### 1.5.7 Determine all values of: #### 1.5.7.1 \( y \) for which \( w(x)<0 \) To find the values of \( y \) for which \( w(x) < 0 \), we need to analyze the function \( w(x) \). This typically involves solving the inequality \( w(x) < 0 \). #### 1.5.7.2 \( x \) for which \( w(x)<-\frac{7}{10} \) Similarly, to find the values of \( x \) for which \( w(x) < -\frac{7}{10} \), we will solve the inequality \( w(x) < -\frac{7}{10} \). ### 1.5.8 If a function is as determined in 2.2, write down the equation (8) of \( v^{-1}(x) \). To find the inverse function \( v^{-1}(x) \), we need to express \( x \) in terms of \( v(x) \) and then solve for \( v^{-1}(x) \). This requires knowing the specific form of \( v(x) \). ### 1.5.9 If \( h(x)=w(x)-\sqrt{x} \) where the range of \( \sqrt{x} \) is \( (0 ; \infty) \), calculate the range of \( h(1) \). To find the range of \( h(1) \), we will evaluate \( h(1) = w(1) - \sqrt{1} \). This requires knowing the value of \( w(1) \). ### Next Steps To proceed with the calculations for parts 1.5.7.1, 1.5.7.2, and 1.5.9, I need the specific forms of the functions \( w(x) \) and \( v(x) \). Please provide these functions or any additional information needed to solve the inequalities and evaluate \( h(1) \).