If you were given the function f(x) and its inverse function,
, what would you expect the values of
to be, assuming that 3 is part of the domain of f(x)? Explain your answer.

3

Step-by-step explanation:

if we combine a function f(x) and its inverse f-¹(x), the result will be x

f-¹(f(x)) = f(f-¹(x)) = x

you can try for any function, i.e.

f(x) = 2x + 1

f-¹(x) = (x-1)/2

f-¹(f(x)) = (2x + 1 - 1)/2 = x

f(f-¹(x)) = 2((x-1)/2) + 1 = x - 1 + 1 = x

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.