Hey there! :)
Answer:
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
Step-by-step explanation:
Given:
f(x) = 5x² + 2
Switch the x and y variables in the equation:
x = 5y² + 2
Subtract 2 from both sides:
x - 2 = 5y²
Divide 5 from both sides:
[tex]\frac{1}{5}(x-2) = y^{2}[/tex]
Square root both sides:
y = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
**Make sure to add a ± sign when finding the inverse of a parabolic function.
Therefore, the inverse of this function is:
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
