Question

find the inverse of the function. Is the inverse a function?

y = 5x^2 + 2

Answer 1

f^-1 (x)= sqrt(5x)/ sqrt(5x),  -sqrt(5x)/5 is the inverse of the function y=5x^2

Answer 2

to find the inves
solve for x and replace x with finverse and  y with x

y=5x^2+2
minus 2
y-2=5x^2
divide by 5
(y-2)/5=x^2
sqrt both sides
$x= \sqrt{\frac{y-2}{5} }$
$x= \frac{ \sqrt{ y-2}}{ \sqrt{5} }$
$x= \frac{ \sqrt{5( y-2)}}{5 }$
$x= \frac{ \sqrt{5y-10}}{5 }$
inverse
$f(x)^{-1}= \frac{ \sqrt{5x-10}}{5 }$
for it to be a function, every x must corespond to exactly 1 y
seems to corespond to 1 each
it is a function