Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/x-1

f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)

To confirm that f(x) and g(x) are inverses.

f(g(x)) = x

g(f(x)) = x

f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)

f(g(x)) = (-15x² -15x)/(-15x² - 15)

f(g(x)) = -15x/-15

f(g(x)) = x

g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)

g(f(x)) = (-15x² - 105x)/(-15x²- 105)

g(f(x)) = -105x/-105

g(f(x)) = x

f(x) and g(x) are inverses.

∠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.

step-by-step explanation: