Triangle QNP was dilated by a scale factor of One-third about point P. It was then transformed in another way to produce Triangle Q prime N prime P prime.

On a coordinate plane, triangle Q N P has points (negative 1, 0), (negative 7, 9), (negative 1, 9). Triangle Q prime N prime P prime has points (6, 1), (9, 3), (9, 1).

Which identifies the transformation that occurred after the dilation?
a 90 degrees clockwise rotation about the origin
a 180 degrees clockwise rotation about the origin
a reflection across the x-axis
a reflection across the y-axis

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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