 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that graph f of x is equal to x cube plus 1, find its inverse and draw its graph, show solution points for both functions. We know that if f of x is a function whose inverse is given by f inverse then the graph of f inverse is obtained by reflecting the graph of f across the line y is equal to x, reflection points in line y is equal to x is given by the point which coordinates x, y is transformed to the point that is if the point with coordinates x, y lies on graph of f of x then the point with coordinates y, x will lie on graph of f inverse. With this key idea we shall proceed to the solution. Now it is given in the question that we have to graph the function given by the equation f of x is equal to x cube plus 1. Now let us make its table of values. We can also write this function as y is equal to x cube plus 1 and now when we put the value of x as minus 1 we get the value of y as y is equal to minus 1 whole cube plus 1 which implies that y is equal to minus 1 plus 1 which is equal to 0. So for x is equal to minus 1 y is 0. Similarly when we put the value of x as 0 we get the value of y as 0 cube plus 1 which implies that y is equal to 0 plus 1 that is equal to 1. So for x is equal to 0 y is 1. Similarly we obtained different values of y for the corresponding values of x that is when x is equal to 1 y is equal to 2, when x is equal to 2 y is equal to 9 and when x is equal to 1 by 2 y is 9 upon 8. Now we shall plot these points on the coordinate plane. Now we have plotted these points on the coordinate plane. Here we have this point with coordinates minus 1, 0. This point with coordinates 0, 1. Here is the point with coordinates 1 by 2, 9 by 8. This is the point with coordinates 1, 2 and this is the point with coordinates 2, 9. Now we shall join these points with a free hand curve. This is the required graph of the function f of x is equal to x cube plus 1. Now let us find its inverse. Now to find its inverse first we replace f of x in this equation by y. So we have y is equal to x cube plus 1. Now we switch x and y and we get x is equal to y cube plus 1. Now we shall solve this equation for y and we get x minus 1 is equal to y cube. Now taking cube root we get cube root of x minus 1 the whole is equal to y or we can write it as y is equal to cube root of x minus 1 the whole. Now we replace y by f inverse of x and we get f inverse of x is equal to cube root of x minus 1 the whole and now we shall graph this inverse function which is given by cube root of x minus 1 the whole. From the key idea we know that if f of x is a function whose inverse is f inverse then the graph of f inverse is obtained by reflecting the graph of f across the line y is equal to x. So graph of f inverse of x will be the reflection of the graph f of x across the line y is equal to x. So let us draw the line y is equal to x. Now this is the line which shows the graph of the equation y is equal to x. Now we shall draw its table of values for this we interchange the values of x and y in the above table and the new table we get will be the table of values for the inverse function. So this is the required table of values for the inverse function f inverse of x is equal to cube root of x minus 1 the whole. Now we shall plot these points on the coordinate plane. Now here we have plotted these points on this coordinate plane and now we join these points by a free hand curve and this is the required function for the inverse graph given by f inverse of x is equal to cube root of x minus 1 the whole. The solution points for the function f of x is equal to x cube plus 1 are given by the ordered pairs minus 1 0 0 1 1 2 2 9 and 1 by 2 9 by 8. The solution points for the inverse function f inverse of x is equal to cube root of x minus 1 the whole are given by the ordered pairs 0 minus 1 1 0 2 1 9 2 9 by 8 1 by 2. This is the required answer. This completes our session. Hope you enjoyed this session.