 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Find the domain and range of the function f of x is equal to minus 4 into 2 upon 7 hold waste to the power x minus 5. Now let us start with the solution of the given question. Here we are given the function f of x is equal to minus 4 into 2 upon 7 hold waste to the power x minus 5. This is an exponential function of the form f of x is equal to a into b waste to the power x plus k. So here in this function we have the value of a as minus 4 and the value of k as minus 5. We have to find its domain and range. We know that for exponential function of the form f of x is equal to a into b waste to the power x plus k where b is greater than 0 and b is not equal to 1. Then if the value of a is less than 0 then domain is set of all real numbers that is open interval from minus infinity to infinity and range is set of all values less than k or y is less than k that is open interval from minus infinity to k. So here domain is given by set of all real numbers that is open interval from minus infinity to infinity. Now a is equal to minus 4 which is less than 0. So range will be equal to set of all values less than minus 5 or y is less than minus 5 that is the open interval from minus infinity to minus 5. Now let us see its graph. Now see here x can take any real value so its domain is set of all real numbers that is the open interval from minus infinity to infinity. For the range we have to see y values. Now we can see that the curve does not lie above y is equal to minus 5. Also if we draw a horizontal line at y is equal to minus 5 the curve does not intersect that line. The curve is moving downwards for negative values of y less than minus 5 so values of y can be from minus infinity to minus 5. So its range is all negative values less than minus 5 or y is less than minus 5 that is the open interval from minus infinity to minus 5. This is the required answer. This completes our session. Hope you enjoyed this session.