If g is the inverse of f and f(2)=4, what is f(2)+g(4)?

The answer is 6.

When we create an inverse equation, all of the outputs become the inputs for the new equation. Therefore any time we put in a number into f(x) for x and got out y, those would be opposite in the g(x) equation. Since when we put in 2 into f(x) we get 4 out, when we put 4 into g(x), we get 2 out. Knowing this we know the following:

f(2) = 4

g(4) = 2

So when we add those two together, we get 6.

∠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.