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

Question

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

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

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

y=85(x+2)
y equals Start Fraction 8 over 5 End Fraction left parenthesis x plus 2 right parenthesis

y=15(8x+2)

Answer 1

To find the inverse relation of \( f(x) = (5x - 2)8 \) algebraically, we start by letting \( y = f(x) \):

\[ y = (5x - 2)8 \]

Next, we will solve for \( x \) in terms of \( y \):

1. Divide both sides by 8:

\[ \frac{y}{8} = 5x - 2 \]

2. Add 2 to both sides:

\[ \frac{y}{8} + 2 = 5x \]

3. Divide both sides by 5 to solve for \( x \):

\[ x = \frac{\frac{y}{8} + 2}{5} \]

Now we can simplify this expression:

\[ x = \frac{y + 16}{40} \]

To express the inverse function, we swap \( x \) and \( y \):

\[ y = \frac{x + 16}{40} \]

So the inverse function is:

\[ f^{-1}(x) = \frac{x + 16}{40} \]

However, none of the provided responses match this calculation directly. Based on your initial function, it seems there may have been a misunderstanding or a need to re-check the problem setup or the function.

If \( f(x) = 8(5x - 2) \), the correct inverse would be found as shown. Otherwise, please clarify the setup for more precision.