Identify the inverse g(x) of the given relation f(x).f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

Answer:The inverse g(x) = 2x + 2Step-by-step explanation:* Lets explain the inverse of a function- To find the inverse of any function we switch the x and y then  we solve to find the new y- The domain of the function is the values of x and the range of  the function is the values of y- The domain of the inverse function is the values of y and the  range of the inverse function is the values of x- Lets solve the problem∵ f(x) = {(8 , 3) , (4 , 1) , (0 , -1) , (-4 , -3)}- To find the inverse g(x) lets find f(x) from the order pairs∵ x-coordinates are decreases by 4 and y-coordinates are   decreases by 2∴ The relation represents the linear function- The form of the linear function is f(x) = mx + c , where m is the   slope of the line and c is the y-intercept∵ The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)   is m = (y2 - y1)/(x2 - x1)- We can find the slope from any two order pairs∵ (x1 , y1) = (8 , 3) and (x2 , y2) = (4 , 1)∴ m = [1 - 3]/[4 - 8] = -2/-4 = 1/2∵ f(x) = mx + c∴ f(x) = 1/2 x + c- The y-intercept means the line intersect the y-axis   at point (0 , c)∵ There is a point (0 , -1)∴ c = -1∴ f(x) = 1/2 x - 1- To find the inverse of the function switch x and y and solve to   find the new y∵ y = 1/2 x - 1 ⇒ switch x and y∴ x = 1/2 y - 1 ⇒ add 1 to both sides∴ x + 1 = 1/2 y ⇒ Multiply both sides by 2∴ 2(x + 1) = y∴ y = 2x + 2∵ g(x) is the inverse of f(x)∵ The inverse of f(x) is 2x + 2∴ g(x) = 2x + 2