Answer:
[tex]\large\boxed{(f\circ h)(4)=2}[/tex]
Step-by-step explanation:
[tex](f\circ h)(x)=f\bigg(h(x)\bigg)-\text{subtitute}\ x=h(x)\ \text{into}\ f(x).\\\\\bold{METHOD\ 1:}\\\\\text{Calculate}\ h(4):\\\\\text{Put}\ x=4\ \text{to the equation of}\ h(x):\\\\h(4)=-4+3=-1\\\\\text{Put the value of}\ h(4)\ \text{to the equation of}\ f(x):\\\\x=-1\to f\bigg(h(4)\bigg)=-3(-1)-1=3-1=2[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{Put}\ x=h(x)\ \text{th the equation of }\ f(x):\\\\f\bigg(h(x)\bigg)=-3(-x+3)-1\qquad\text{use the distributive property}\\\\f\bigg(h(x)\bigg)=(-3)(-x)+(-3)(3)-1\\\\f\bigg(h(x)\bigg)=3x-9-1\\\\f\bigg(h(x)\bigg)=3x-10\\\\\text{Put}\ x=4\ \text{To the equation of}\ f\bigg(h(x)\bigg):\\\\f\bigg(h(4)\bigg)=3(4)-10=12-10=2[/tex]
