Determine the roots of f(x) = -x2 - 2x2 + 5x + 6.

2.1 Given the following set of ordered pairs for f(x): \(-2; 3), (0; -1), (1; 2), (2; 0)\. 2.1.1 Write the inverse, f^-1(x) as a set of ordered pairs. Step 1: To find the inverse of a set of ordered pairs, swap the x and y coordinates for each pair. f^-1(x) = \(3; -2), (-1; 0), (2; 1), (0; 2)\ The final answer is: f^-1(x) = \(3; -2), (-1; 0), (2; 1), (0; 2)\ 2.1.2 State whether f(x) is a function or a non-function. Step 1: A relation is a function if each input (x-value) has exactly one output (y-value). The x-values in f(x) are -2, 0, 1, 2. Each x-value is unique and corresponds to only one y-value. The final answer is: Function 2.2 The figure below represents the graph of g(x): y = a^x with domain x R. Point A lies on g(x) and the co-ordinates of A are (4; 8). 2.2.1 Determine the equation for g(x) and leave the answer in the form y = ... Step 1: Substitute the coordinates of point A(4; 8) into the equation y = a^x. 8 = a^4 Step 2: Solve for a. a = [4]8 a = (2^3)^(1)/(4) a = 2^(3)/(4) Step 3: Write the equation for g(x). y = (2^(3)/(4))^x y = 2^(3x)/(4) The final answer is: y = 2^(3x)/(4) 2.2.2 Determine the equation of g^-1(x). Give the answer in the form x = ... Step 1: Start with the equation for g(x): y = 2^(3x)/(4). Step 2: To find the inverse, swap x and y. x = 2^(3y)/(4) This equation is already in the requested form x = .... The final answer is: x = 2^(3y)/(4) 2.2.3 Write down an equation for the asymptote of g^-1(x). Step 1: The original function g(x) = 2^(3x)/(4) is an exponential function. Exponential functions of the form y = b^x have a horizontal asymptote at y=0. Step 2: The inverse function g^-1(x) is a logarithmic function. The asymptote of an inverse function is found by swapping the variables in the asymptote of the original function. If the asymptote for g(x) is y=0, then the asymptote for g^-1(x) is x=0. The final answer is: x = 0 That's 2 down. 3 left today — send the next one.