Question

Given the function f left parenthesis x right parenthesis equals StartRoot x minus 10 EndRoot
​,
​(a) Find f Superscript negative 1 Baseline left parenthesis x right parenthesis
.
​(b) Graph f and f Superscript negative 1

in the same rectangular coordinate system.
​(c) Use interval notation to give the domain and the range of f and f Superscript negative 1
.
​(Hint: To solve for a variable involving an nth​ root, raise both sides of the equation to the nth​ power, left parenthesis RootIndex n StartRoot y EndRoot right parenthesis Superscript n Baseline equals y
​.)

Answer 1

$\\(a)\\ \text{Consider the function, }\\ \\ f(x)=\sqrt{x-10}\\ \\ \text{let }y=f(x)\\ \\ \text{so in order to find the inverse function, first we interchange x and y.}\\ \text{so we have}\\ \\ x=\sqrt{y-10}\\ \\ \text{now we solve for y and that will give the required inverse function.}\\ \\ \text{square both sides to get} \\ \\ x^2=(\sqrt{y-10})^2\\ \\ \Rightarrow x^2=y-10\\ \\ \Rightarrow y=x^2+10\\ \\ \text{so the inverse function is }\\ \\ f^{-1}(x)=x^2+10.$

$\\(b)\\ \text{The graphs of f and }f^{-1} \text{ are shown below:}\\ \\ (c)\\ \text{from the graph of f(x), we can see that}\\ \\ \text{Domain}=[10,\infty)\\ \\ \text{Range}=[0,\infty)\\ \\ \text{and from the graph of inverse function }f^{-1}(x), \text{ we can see that}\\ \\ \text{Domain}=[0, \infty)\\ \\ \text{Range}=[10, \infty)$

Answer 2

Answer:

What are the roots of f(x) = x2 – 48?

–48 and 48

–24 and 24

Negative 8 StartRoot 3 EndRoot and 8 StartRoot 3 EndRoot

Negative 4 StartRoot 3 EndRoot and 4 StartRoot 3 EndRoot

THE ANSWER IS D