Question

Help please<3 for all questions with solutions plz

Answer 1

a)
`h = -(7)/(4)`, b)
`h = f\,\circ\,g (-5) = (3)/(2)`, c)
`h = g\,\circ\,f (-2) = (3)/(8)`

Explanation:

We proceed to solve each exercise below:

a)
`f(-2) +3\cdot g(0)`

`h = (2\cdot (-2))/(3\cdot (-2)+5)+3\cdot \left((3)/(0+4) \right)`

`h = (-4)/(-6+5) +3\cdot \left((3)/(4) \right)`

`h = -4+(9)/(4)`

`h = (-16+9)/(4)`

`h = -(7)/(4)`

b)
`h = f\,\circ \,g (-5)`

`h = f\,\circ\,g (x) = ((6)/(x+4) )/((9)/(x+4)+5 )`

`h = f\,\circ\,g (x)= ((6)/(x+4) )/((9+5\cdot (x+4))/(x+4) )`

`h = f\,\circ\,g (x) = (6)/(29+5\cdot x)`

`h = f\,\circ\,g (-5) = (6)/(29+5\cdot (-5))`

`h = f\,\circ\,g (-5) = (3)/(2)`

c)
`h = g\,\circ\,f(-2)`

`h = g\,\circ \, f (x) = (3)/((2\cdot x)/(3\cdot x + 5) + 4 )`

`h = g\,\circ\,f (x) = (3)/((2\cdot x +4\cdot (3\cdot x +5))/(3\cdot x +5 ) )`

`h = g\,\circ \,f (x) = (3\cdot (3\cdot x +5))/(2\cdot x +12\cdot x +20)`

`h = g\,\circ\,f(x) = (9\cdot x +15)/(14\cdot x +20)`

`h = g\,\circ\,f(-2) = (9\cdot (-2)+15)/(14\cdot (-2)+20)`

`h = g\,\circ\,f (-2) = (-3)/(-8)`

`h = g\,\circ\,f (-2) = (3)/(8)`