Answer
a. Yes, it is a one-to-one function
b. See graph below in purple
c. See graph below in blue
d. $(x-1)^4 = f^{-1} (x)$
Work Step by Step
a. $f(x) = 1 + \sqrt[4] {x}$
$f(p) = 1 + \sqrt[4] {p}$
$f(q) = 1 + \sqrt[4] {q}$
$f(p) = f(q)$
$1 + \sqrt[4] {p} = 1 + \sqrt[4] {q}$
$\sqrt[4]{p} = \sqrt[4] {q}$
$p=q$
Thus, it is a one-to-one function
b. See graph below. This graph will be in purple
$f(x) = 1 + \sqrt[4] {x}$
c. This question asks for the graph of the inverse of f(x). See graph below. This graph will be in blue.
d. To find the inverse of f(x), reflect the equation over the line y=x
$x = 1 + \sqrt[4] {y}$
$x-1 = \sqrt[4]{y}$
$(x-1)^4 = f^{-1} (x)$