Ginoni the goat is at the bottom of a series of 7 boulders, each higher than the last. She wants
to reach the top, where there is a huge patch of
grass that she’d like to graze. Being an athletic
goat, she sometimes bounds up two boulders at
a time; otherwise, she just jumps up one.

Ginoni can use both one-boulder and two-
boulder leaps within an ascent.

Starting at the bottom, in how many ways could
she reach the grass at the top?
Investigate what happens for different numbers
of boulders and explain the pattern of how many
different ways she can ascend.

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7

first the equation needs to be simplified. so the equation would now look like:   52-24+11

then you multiply.

and when you multiply, you will get the answer of 39.