Find the domain of f?

Question

Let f be given by the formula:

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Answer 1 · 2018-03-01T12:02:53

#(-oo,-3)uu(1,oo)#

The domain is defined as all possible values of #x# for which #f(x)# will be defined.

Here, as #x^2+2x-3rarr0#, #f(x)rarr+-oo# .

We can say that #f(x)# is undefined when #x^2+2x-3=0#. Solving for #x#:

#x^2+2x-3=0#

#x^2+3x-x-3=0#

#x(x+3)-1(x+3)=0#

#(x+3)(x-1)=0#

So #f(x)# is undefined when #x=1# and #x=-3#.

In interval notation, we can write this as:

#(-oo,-3)uu(1,oo)#