Determine the following composite functions

[bomdia22]

Determine x in the case below, knowing that angle A is a right angle, B is angle 2x+5, C is angle x+1, D is angle 3x-10, E is angle 3x.

Knowing the functions f(x) = 2x − 1 and g(x) = x2 + 7, determine the following composite functions:

a)f ∘ g
b) g ∘ g
c) g ∘ f
d) f ∘ f

[shyamjayakannan]

1) the sum of the interior angles [tex]=180 ^\circ(n-2)[/tex], where [tex]n[/tex] is the number of sides of a convex polygon.
So, [tex]90^\circ+(2x+5)+(x+1)+(3x-10)+3x=180 ^\circ (5-2) \Rightarrow \boxed{x=50.44 ^\circ }[/tex]

2)
a) [tex]f(g(x))=2g(x)-1=2(x^2+7)-1=\boxed{2x^2+13}[/tex]
b) [tex]g(g(x))={g(x)}^2+7=\left(x^2+7\right)^2+7=\boxed{x^4+14x^2+56}[/tex]
c) [tex]g(f(x))={f(x)}^2+7=(2x-1)^2+7=\boxed{4x^2-4x+8}[/tex]