What is the domain of x=b^y?

b^y is always greater than 0

f(-1) is undefined.

(a) Consider that y is a function of x.
x=b^y=>
yln(b)=ln(x)=>
y=ln(x)/ln(b)
=>
dom(y)={x | x is real & x>0}

(b) f(x)=1/(x+1)
limit f(x)=infinity
x->-1
Infinity is not a finite nor definite value, so
f(x) is discontinuous at x=-1, By definition,
if f(x) is continuous at x=a, then
limit f(x)=f(a)
x->a
where f(a) exists & is a finite & definite value.

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