Question

Which two of the three functions are inverses of one another? Explain how you verified that two functions are inverses of one another using composition of functions and show your math work.

f (x) = ³√ x- 4 ( imagine if the tip of the symbol went to the end at 4 )

g(x) = x³ − 4

h(x) = x³ + 4

Answer 1

$f(g(x))=\sqrt[3]{x^3-4-4}=\sqrt[3]{x^3-8} \not=x$

f(x) and g(x) are not inverses

$f(h(x))=\sqrt[3]{x^3+4-4}=x$

f(x) and h(x) are inverses