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

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Answer 1 · 2018-07-24T06:11:48

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

Using interval notation:

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

#" "#
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+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.