Thread: 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 there anyone who knows i'm quite stuck here =/

this is as far as i have come =/

y = f(u)
u = g(x)

if we incorporate u= g(x) in to y = f(u) we get y = f(g(x)) which is one step closer to y= x * f(g(x)) but from here i can't really use a valid formula that allows me to go any further. I was thinking y2 - y1 = k(x2 - x1) or also y = kx+b

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!