Use algebra to find the inverse of the function \( f(x)=5 x^{5}+4 \) The inverse function is \( f^{-1}(x)= \)
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To find the inverse of the function \( f(x) = 5x^5 + 4 \), start by replacing \( f(x) \) with \( y \): \[ y = 5x^5 + 4 \] Next, swap \( y \) and \( x \): \[ x = 5y^5 + 4 \] Now, solve for \( y \). First, isolate the term with \( y \): \[ x - 4 = 5y^5 \] Then, divide by 5: \[ \frac{x - 4}{5} = y^5 \] Finally, take the fifth root of both sides: \[ y = \sqrt[5]{\frac{x - 4}{5}} \] Thus, the inverse function is: \[ f^{-1}(x) = \sqrt[5]{\frac{x - 4}{5}}. \] This gives you the formula for the inverse function.