Question

Please help me figure out this problem

Answer 1

`f(g(x))=f\left(-(3x+21)/(5)\right)=x\\\\g(f(x))=g\left(-(5)/(3)x-7\right)=x`

Explanation:

Fill in the given expressions and simplify.

`f(g(x))=f\left(-(3x+21)/(5)\right)=-(5)/(3)\left(-(3x+21)/(5)\right)-7\\\\=\left(-(5)/(3)\right)\left(-(3x)/(5)\right)-\left((5)/(3)\right)\left(-(21)/(5)\right)-7\\\\=(15x)/(15)+(5\cdot 21)/(3\cdot 5)-7=x+7-7=x`

Going the other way, we have ...

`g(f(x))=\displaystyle -(3\left(-(5)/(3)x-7\right)+21)/(5)=-(-5x-21+21)/(5)=x`