Answer all the questions below for your SOB to be observed. You might be asked to explain them verbally. We rely on the following function composition definition: (fog)(x) = f(g(x)). Example: Let f(x) 3x and g(x)-2x + 1 (with f and g defined from RR). then (fog)(x)f(g(x)) f(2x + 1)-3(2x + 1) = 6x +3. Consider the following function: f:R R f(x) - cos() Classify this relation and explain why it is a function? What can you say about ran(f)? Let f : WT and g:S W be two functions. Prove, relying on a mathematical reasoning, that the target of (fog) will be the target off but the range of (f o g) is not necessarily the range of f. Consider the following function: f:Z Z f(x) - x+3 Is f one-to-one? Is f total? If not, how could you modify the signature of f to make it total. Let f(x) and g(x)-x-4 where f,g: R+ 4 > R. Formulate (gog)(x). (fog)(x). (go f)(x). For each of these functions, indicate if it is or not total. Justify your answers using a mathematical reasoning. Let f WT and g: SW. Demonstrate, using a mathematical reasoning, that (fog) is one-to-one f is one-to-one but (fog) is one-to-one f is one-to-one. Activate Wind se to Settings to a