Interactive practice questions
Consider the function $f\left(x\right)=x^2-8x+11$f(x)=x2−8x+11.
Graph the function on the axes below:
Is the function $f\left(x\right)=x^2-8x+11$f(x)=x2−8x+11 a one-to-one function?
No
Yes
Although the function is not one-to-one, if we restrict the domain we can find a portion of the function that is one-to-one.
Which of the following domains are appropriate restrictions for $f\left(x\right)$f(x) to be a one-to-one function?
Select all that apply.
$\left[1,\infty\right)$[1,∞)
$\left[4,\infty\right)$[4,∞)
$\left(-\infty,8\right]$(−∞,8]
$\left(-\infty,4\right]$(−∞,4]
Find the inverse function $f^{-1}\left(x\right)$f−1(x) for $f\left(x\right)$f(x) on the restricted domain $\left[4,\infty\right)$[4,∞), by replacing $x$x with $y$y and $f\left(x\right)$f(x) with $x$x solving for $y$y.
Select all the functions that are one-to-one.
Which of the following describes the inverse of a function that is one-to-one?
Consider the graph of each function below and determine if it has an inverse function.