Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points)
f(x) = x2 - 3 and g(x) = square root of quantity three plus x

f(g(x)) = g(f(x))  = x and f and g are the inverses of each other.

Step-by-step explanation:

Here, the given functions are:

To Show:  f (g(x))  = g (f (x))

(1)  f (g(x))

Here, by the composite function:

⇒ f (g(x))  = x

(2) g (f(x))

Here, by the composite function:

⇒ g (f(x))  = x

Hence, f(g(x)) = g(f(x))  = x

⇒ f and g are the inverses of each other.

∠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.