find the domain pls

Question

Find the domain of the following :

 

f(x) = 1-1/x^2/1+√(2x-4)^2

 

and

 

g(x) = √t+3 / t-t^3

 

and thank you !

Answer 1

Use parentheses!  I'm can't tell what the equations really are.

f(x) = 1-1/x^2/1+√(2x-4)^2

 

f(x) = [1-(1/x^2)] / [1+√(2x-4)]^2

or

f(x) = [1-(1/x)^2] / [1+√(2x-4)^2]

or

f(x) = [1-(1/x)^2] / [1+√(2x-4)]^2

or a few other possibilities.

 

To find the domains, you need to look at all denominators.  No denominator can be equal to zero because division by zero is undefined.

 

For example if, (t-t^3) is a denominator, you need to find what value(s) of t would make it zero.

Solve this to find those values:

t-t^3 = 0

(t)(1-t^2) = 0

(t)(1+t)(1-t) = 0

This would be zero for t=0, t=-1, or t=1.

Exclude those values from the domain.

 

Domain = (-∞,-1) U (-1, 0) U (0, 1) U (1, ∞)

 

If there is a 1/x somewhere, x cannot be zero.

etc...

 

Important note: You have to look at the original form of the equation.  No simplifying first. A common factor in a numerator and denominator might cancel out when you simplify.

 

[(x)(x-1)] / x simplifies to just x-1, but the original form has a division by x, so x=0 must be excluded.

 

Does this help?