Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q25

Answer 1

The function given is,

`f(x)=(4)/(7+x)`

Let us now find the inverse of the above function

`\mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)`

Replace x with y

`x=(4)/(7+y)`

Solve for y

`\begin{gathered} x(7+y)=4 \\ (x(7+y))/(x)=(4)/(x) \\ 7+y=(4)/(x) \\ \therefore y=(4)/(x)-7 \end{gathered}`

Therefore,

`f^(-1)(x)=(4)/(x)-7`

Domain of f(x) is

`\lbrace x|x\\e-7\rbrace\text{ Option B}`

Range of f(x) is

`\lbrace y|y\\e0\rbrace\text{ Option B}`

Domain of the inverse function

`\lbrace x|x\\e0\rbrace\text{ Option C}`

Range of the inverse function

`\lbrace y|y\\e-7\rbrace\text{ Option C}`