A function g(x) =2x+5÷x-2 for all values of x except x=2.Show that g(g(x))=x.
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Given f(x) = 2x + 3 and g(x) = –x2 + 5, find ( f o f )(x).

( f o f )(x) = f ( f (x))

   = f (2x + 3)

   = 2(           ) + 3    ... setting up to insert the input

   = 2(2x + 3) + 3

   = 4x + 6 + 3

   = 4x + 9

Given f(x) = 2x + 3 and g(x) = –x2 + 5, find (g o g)(x).

(g o g)(x) = g(g(x))

   = –(             )2 + 5     ... setting up to insert the input

   = –(–x2 + 5)2 + 5

   = –(x4 – 10x2 + 25) + 5

   = –x4 + 10x2 – 25 + 5

   = –x4 + 10x2 – 20

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.