 Hello and welcome to the session. In this session we discuss the following question which says find H O G O F given the following functions F which goes from R to R such that F X is equal to X to the power 5 G which goes from R to R such that G X is equal to sec X, H which goes from R to R such that H X is equal to log of X. Also find the value of H O G O F of 0. Let's see the solution now. We have a function F which goes from R to R such that we have F X is equal to X to the power 5 then a function G which goes from R to R where G X is equal to sec X function H which goes from R to R such that H X is equal to log X. We have to find out H O G O F now let X be an arbitrary real number then first let's find out G O F of X this would be equal to G of F X. Now F X is equal to X to the power 5 so this is equal to G of X to the power 5 now G X is equal to sec X so this is equal to sec X to the power 5 this is G O F of X. Now H O G O F of X is equal to H of G O F of X that is this is equal to H of sec X to the power 5 since we have G O F of X is equal to sec X to the power 5 now since H X is equal to log X so in place of X here we put sec X to the power 5 so we get log sec X to the power 5 this is H O G O F of X thus the value for H O G O F is equal to log sec X to the power 5 we also have to find the value of H O G O F of 0 so in place of X here we put 0 so we have H O G O F of 0 would be equal to log sec 0 so this is equal to log of 1 since sec 0 is equal to 1 and log of 1 is equal to 0 thus we get H O G O F of 0 is equal to 0 so we have got the value of this as 0 so this completes this session hope you have understood the solution of this question.