Question

Let ​f(x)equals=33xminus−​1, ​h(x)equals=startfraction 7 over x plus 5 endfraction 7 x+5 . find ​(hcircle◦​f)(66​).

Answer 1

$\bf \begin{cases} f(x)=3x-1\\ h(x)=\cfrac{7}{x+5}\\\\ (h\circ f)(x)=h(~~f(x)~~) \end{cases} \\\\\\ f(66)=3(66)-1\implies \boxed{f(66)=197} \\\\\\ \stackrel{h(~~f(x)~~)}{h(~~f(66)~~)}\implies \stackrel{h(~~f(66)~~)}{h\left(~~\boxed{197}~~ \right)}=\cfrac{7}{\boxed{197}+5}\implies h\left(~~\boxed{197}~~ \right)=\cfrac{7}{202}$