Question

Two algebraic ecpression that have the same domain and yield the same values for all numbers in their domains are called

Answer 1

When we have two algebraic expression

that will give same result for same domain

both expression would be equivalent of each other

For example:

$f(x)=\frac{x^2-2x-8}{x^2-x-12}$

and

$g(x)=\frac{x+2}{x+3}$

now, when we simplify f(x)

$f(x)=\frac{(x-4)(x+2)}{(x-4)(x+3)}$

$f(x)=\frac{(x+2)}{(x+3)}$

we can see that f(x) and g(x) will become

so, they will give same result for same domain

Hence, f(x) and g(x) are equivalent

so,

Two algebraic expression that have the same domain and yield the same values for all numbers in their domains are called equivalent