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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

1 answer

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.