The spatial coordinates (x,y)(x, y)(x,y) of a particle moving through a controlled force field are defined by the parametric equations
x=5t−7y=6t−24t+3t>0 x = \frac{5}{t} - 7 \quad y = \frac{6t - 2}{4t + 3} \quad t > 0 x=t5−7y=4t+36t−2t>0Show that the equation of the trajectory can be written in the form y=g(x)y = g(x)y=g(x) where g g\,g is the function
g(x)=ax+bcx+dx>k g(x) = \frac{ax + b}{cx + d} \quad x > k g(x)=cx+dax+bx>kwhere a,b,c,d a, b, c, d\,a,b,c,d and k k\,k are integers to be found.
Hence, or otherwise, state the range of ggg.
