Given:
[tex]f(x)=11-\frac{x}{4},h(x)=-4(x-11)[/tex]
To show the given functions are inverses of each other, they must satisfy the following conditions,
[tex]\begin{gathered} (f\circ h)(x)=x \\ (h\circ g)(x)=x \end{gathered}[/tex]
Now,
[tex]\begin{gathered} (f\circ h)(x)=f(h(x)) \\ =f(-4(x-11)) \\ =11-\frac{(-4(x-11))}{4} \\ =11+(x-11) \\ =x \end{gathered}[/tex]
And,
[tex]\begin{gathered} (h\circ g)(x)=h(f(x)) \\ =h(11-\frac{x}{4}) \\ =-4((11-\frac{x}{4})-11) \\ =-4(11-\frac{x}{4}-11) \\ =x \end{gathered}[/tex]
It shows that the given functions are inverses of each other.
Answer:
[tex]\begin{gathered} f\mleft(h\mleft(x\mright)\mright)=x \\ h(f(x))=x \end{gathered}[/tex]
Yes. the given functions are inverses of each other.
