Problemas
Is the inverse a function? f(x)=(x+5)^3 D yes no Write the inverse function in the form a . sqrt [3](bx)+c+d , where a, b , c, and d are constants . Simplify any fractions. f^-1(x)=square
Roztwór
Emiliano
experto · Tutor durante 3 años
4.1
(243 Votos)
Respuesta
To determine if the inverse of the function
is also a function, we need to check if the original function is one-to-one. A function is one-to-one if each input corresponds to a unique output and each output corresponds to a unique input.In this case, the function
is one-to-one because for every value of
, there is a unique value of
. Therefore, the inverse of this function will also be a function.To find the inverse function, we need to solve for
in terms of
. Let's start by setting
:
Now, we need to solve for
:
So, the inverse function is:
Therefore, the answer is:D yes