1. To find 'a' when f(g(a)) = 1, you need to determine the value of 'a' that makes the composition of the two functions equal to 1.
Here's an algebraic approach to solving this type of question:
Step 1: Identify the values of 'a' that correspond to points where g(a) equals 1. This means we are looking for values of 'a' where g(a) intersects the line y = 1 on the graph.
Step 2: Once you have identified the values of 'a' from Step 1, substitute them into f(g(a)) and check if it equals 1. This will give you the specific value of 'a' that satisfies the equation.
If you have the graphs of f(x) and g(x) but not the equations, you can use the graphical approach to estimate the values of 'a'. Use the intersection points between g(a) and the line y = 1 to determine the x-coordinates of those points.
2. In the context of positive and negative numbers, 0 is considered to be neither positive nor negative. Therefore, to make both zeros (5 and -1) positive, you would need to shift the graph to the right. Shifting the graph 1 unit to the right would indeed result in new x-intercepts of 6 and 0.