 Hello and welcome to this session. In this session we will discuss the question which says that draw the graph of the function y is equal to 2 raised to power x and its inverse also write the equation of its inverse. Now before starting the solution of this question we should know our result and that is for the function y is equal to f of x the graph of its inverse is given by f inverse which is obtained by reflecting the graph of f across the line y is equal to x. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Let us draw the graph of the function y is equal to 2 raised to power x. Now let us make table of values that is we will put different values of x in this equation and we will get the corresponding values of y first of all let us put x is equal to minus 3 and for x is equal to minus 3 we get y is equal to 1 upon 8 then for x is equal to minus 2 we get y is equal to 1 upon 4 then for x is equal to minus 1 we get y is equal to 1 upon 2 similarly for x is equal to 0 we get y is equal to 2 raised to power 0 that is 1 then for x is equal to 1 we get y is equal to 2 raised to power 1 that is 2 then for x is equal to 2 we get y is equal to 2 raised to power 2 that is 4 and for x is equal to 3 we get y is equal to 2 to power 3 that is 8. Now 1 upon 8 is approximately equal to 0.1, 1 upon 4 is approximately equal to 0.3 and 1 upon 2 is equal to 0.5. Now we will draw all these points on the coordinate plane. Now for x is equal to minus 3, y is equal to 0.1. So we have plotted the point with coordinates minus 3, 0.1. The next point will have coordinates minus 2, 0.3. So this is the point with coordinates minus 2, 0.3. Similarly we will plot all these points on the coordinate plane. So we have plotted all these points on the coordinate plane. Now joining all these points we get an exponential curve and this is the curve of the function y is equal to 2 raise to power x. Now we have to find its inverse. Now let us replace x by y. Now the given function is y is equal to 2 raise to power x. Now to find its inverse let us switch x and y. So its inverse will be given by, now let us solve this equation for y. Now x is equal to 2 raise to power y can be written as log x to the base 2 is equal to y. As we know that y is equal to log x to the base b if and only if b raise to power y is equal to x. Now let us replace y by f inverse of x. So we have f inverse of x is equal to log x to the base 2. Now let us graph the inverse function. Now from t idea we know that graph of the function f inverse is obtained by reflecting the graph of f across the line y is equal to x. Now here let us draw the line y is equal to x and we will interchange x and y in this table which we have obtained earlier. So we have obtained this new table after interchanging the values of x and y. Now let us plot these points on the coordinate plane. So we have plotted all these points on the coordinate plane. Now joining all these points we get this curve which is the graph for the inverse function given by f inverse of x is equal to log x to the base 2. Thus we see that the two halves are mirror images across the line y is equal to x. So this is the solution of the given question. That is all for this session. Hope you all have enjoyed this session.