How do you find the domain of #f(x)=log_8(x+1)#?

1 Answer
Jul 24, 2018

Answer:

#" "#
#color(red)([x>(-1))]# is the required domain of #color(red)(f(x))#

Using interval notation:

#color(red)((-1,oo)#

Explanation:

#" "#
Domain of a function can be defined a s a set of input values for which the function is real and defined .

We are given the function:

#color(blue)(y=f(x)=log_8(x+1)#

Use positive values only for this problem:

#color(red)(x+1>0#

Subtract #color(blue)(1# from both sides

#rArr [(x+1)-1]>0-1#

#rArr [(x+1)-1]>0-1#

#rArr x+1-1>0-1#

#rArr x+cancel 1-cancel 1>0-1#

#rArr x> (-1)#

Hence, our final solution is:

#color(red)([x>(-1))]# is the required domain of #color(red)(f(x))#

Using interval notation:

#color(red)((-1,oo)#

Hope this helps.