Question

Identify the inverse to the function

f(x)=3x4+12
(1 point)
Responses

f−1(x)=4x3−12
f inverse of x is equal to 4 x over 3 minus 1 half

f−1(x)=4x−23
f inverse of x is equal to the fraction with numerator 4 x minus 2 and denominator 3

f−1(x)=3x4−12
f inverse of x is equal to 3 x over 4 minus 1 half

f−1(x)=taco

Answer 1

To find the inverse of the function \( f(x) = 3x^4 + 12 \), we will first set \( y = f(x) \):

1. Start with the equation:
\[
y = 3x^4 + 12
\]

2. Solve for \( x \):
\[
y - 12 = 3x^4
\]
\[
\frac{y - 12}{3} = x^4
\]
\[
x = \sqrt[4]{\frac{y - 12}{3}}
\]

3. Now, to express the inverse function, we switch \( x \) and \( y \):
\[
f^{-1}(x) = \sqrt[4]{\frac{x - 12}{3}}
\]

Looking at the provided options, none of them exactly match this result, but we also recognize that the expression can be written in various forms. Since the function involves a degree of complexity, carefully reviewing for any potential matches would be prudent without introducing errors.

None of the provided options match the derived inverse function. You may need to double-check any conditions that may apply or if there's a miscommunication in the choices offered.