Log functions domain

[helplz]

what up everyone

im stuck on this question and has hoping i could get some help,
so i am given the log function of f(x)=-5log(7x+11)+11
(the log is of base 10 btw if that makes a difference) the first part of the question says that the largest domain of f if x>a what is the value of a? and the second question says suppose b is a number for which both b and 1000b + 10989/7 are in the domain of f(x). find the simplest possible expression for f(1000b + 10989/7 - f(b)?

cheers

 

[Harry_the_cat]

Recall that log(x) is only defined for x>0.
So -5log(7x+11)+11 is only defined when (7x+11)>0. Solve this inequality to get x>? and you'll have "a".

 

[helplz]

Recall that log(x) is only defined for x>0.
So -5log(7x+11)+11 is only defined when (7x+11)>0. Solve this inequality to get x>? and you'll have "a".

right ok thanks so that would mean that a >-11/7 right
and since b and 1000b + 10989/7 are in the domain of f(x) would this mean that i would set f(1000b + 10989/7 - f(b) equal to -11/7 to find the simplest expression

 

[Dr.Peterson]

and since b and 1000b + 10989/7 are in the domain of f(x) would this mean that i would set f(1000b + 10989/7 - f(b) equal to -11/7 to find the simplest expression

There is an unmatched parenthesis in "f(1000b + 10989/7 - f(b)"; I assume you mean "f(1000b + 10989/7) - f(b)". You don't want to set that value to -11/7, but to assume that 1000b + 10989/7 > -11/7 and b > -11/7, and simplify f(1000b + 10989/7) - f(b). The answer will be a single number, as it turns out.