The two(2) given functions are:
[tex]\begin{gathered} f(x)=-5x+9 \\ g(x)=-\frac{1}{5}x-9 \end{gathered}[/tex]
According to definition of Inverse function;
[tex]f\mleft\lbrace g(x\mright)\}=x\text{ and g}\mleft\lbrace f(x\mright)\}=x\text{ if f and g are both inverse of each other}[/tex]
Thus,
[tex]\begin{gathered} f\mleft\lbrace g(x\mright)\rbrack=f(-\frac{1}{5}x-9) \\ \Rightarrow-5(-\frac{1}{5}x-9)+9 \\ \Rightarrow x+45+9 \\ f\mleft\lbrace g(x\mright)\}=x+54 \\ so,\text{ f}\mleft\lbrace g(x\mright)\}\ne x \end{gathered}[/tex]
Hence, they are NOT inverse of each other.
The correct answer is NO
