Question

I NEED help Please

f(a)= -1/4(a+8)

g(b)=2/3b+1

g(f(6))


need help with this composite function

Answer 1

`\large\boxed{g\bigg(f(6)\bigg)=-(4)/(3)}`

Explanation:

`f(a)=-(1)/(4)(a+8)\\\\g(b)=(2)/(3)b+1\\\\g\bigg(f(6)\bigg)\\\\\text{calculate}\ f(6)\to\text{put}\ a=6\ \text{to the equation of}\ f(a):\\\\f(6)=-(1)/(4)(6+8)=-(1)/(4)(14)=-(14)/(4)=-(7)/(2)\\\\g\bigg(f(6)\bigg)\to\text{put}\ b=-(7)/(2)\ \text{to the equation of}\ g(b):\\\\g\bigg(f(6)\bigg)=(2)/(3)\left(-(7)/(2)\right)+1=-(7)/(3)+1=-(7)/(3)+(3)/(3)=-(4)/(3)`