Question

Find the range of function f(x)=㏒2(2-㏒√2(16sin²x+1))
plzz explain also

Answer 1

open bracket minus infinity to 1 close bracket (note some mistake where the sin range is given zero tu 21 by 4 year is no less than or equal to used for 1 by 4 it is only less than)

Answer:

first of all sorry for the poor handwriting

to start the question first of all we need to simplify the log and by using properties of log the expression in IV line is obtained and now we have to find the domain in which the log is defined for the given function as you can see in the the seventh line I have defined 1- log 16 sin square x + 1 base 2 greater than zero and after that I have found the value of sin x less than 1 by 4 and have neglected -1 by 4 because it will also undefine the function and further the range of sin comes out to be zero to 1 by 4 and further the changes are made to make the function as similar to the function given in IV line

Explanation:

(this question is from Balaji advanced mathematics)