Making an equations using 2 functions?

Hi there i'm having some problems with this one can't really figure it out couldn't attach the graphs so i wrote where they hit the y and x axis instead the first is a curve and the other is linear

Make the function y = x * f(g(x)) where the function y=f(g(x)) is defined by two graphs. One of the graphs y = f(u) (the graf is a curve that x-axis on -1 and the y-axis on just around 0.25 and 3.75) has the tangents where u = 1 and u = 3 and the other graph is named u = g(x) (the graf is linear and hits the y-axis on 2.5). The graph for the equations y = x* f(g(x)) has the tangent x = 1. Define the equation for the tangent

/Mathmen

Is this the right answer?

After sitting with the question for a couple of hours a came to this answer, i would really appreciate if anyone can tell me if i made any type of misstake during the process because i'm quite confused if it should actually become y2 = x + f(g(1)) or y2 = x* f(g(1))

Y2 –y 1 = k(x2 –x1)

Y2 – f(g(1)) = f’(g(1)) * g(1) (x2 -1)

y2 – f(g(1)) = f’(g(1)) * g(1) * x - f’(g(1)) * g(1)

Y2 = f’(g(1)) * g(1) * x - f’(g(1)) * g(1) + f(g(1))

y2 = x* f(g(1))

Thanks!