Find the inverse relation of f(x)=(5x−2)8

Question

algebraically by letting y=x
.(1 point)
Responses

y=15(8x+2)
y equals Start Fraction 1 over 5 End Fraction left parenthesis 8 x plus 2 right parenthesis

y=(8x−2)5
y equals Start Fraction left parenthesis 8 x minus 2 right parenthesis over 5 End Fraction

y=(5x+2)8
y equals Start Fraction left parenthesis 5 x plus 2 right parenthesis over 8 End Fraction

y=85(x+2)

Answer 1

To find the inverse relation of the function \( f(x) = (5x - 2)^8 \) algebraically, we follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = (5x - 2)^8 \]

2. Swap \( x \) and \( y \) (this is the step to find the inverse): \[ x = (5y - 2)^8 \]

3. Solve for \( y \): To isolate \( y \), we can first take the eighth root of both sides: \[ x^{1/8} = 5y - 2 \] Next, add 2 to both sides: \[ 5y = x^{1/8} + 2 \] Finally, divide by 5: \[ y = \frac{x^{1/8} + 2}{5} \]

Thus, the inverse function is: \[ y = \frac{x^{1/8} + 2}{5} \]

To summarize, none of the given response options match the calculated inverse. However, using the correct steps, we determined the inverse algebraically. If you find any discrepancies with the provided responses, that would warrant further investigation into the source of those options.