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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

answer: the value of b is 24 + 3t / (4- t ) = b

solution:

step 1 : find the slope using the formula below with the c (t, 3) and d(4, -3)

m = y2-y1 / x2 - x1

m = -3 -3 / 4-t

m = -6/4-t

to find the value of   b use the equation given in the question

note : use any of the pair given c or d in the equation to find the value of b i will be using d ( 4, -3)

y = mx+ b

3 = (-6/4-t)(4) + b don't forget to take the lcm

b = (36 - 3 t ) / ( 4 - t )