Question

find the inverse of the function y=2x^2

Answer 1

to find the inverse  exchange the x and y and then solve for y

y =2x^2

x =2y^2

divide by 2

x/2 = y^2

take the square root of each side

sqrt(x/2) =y

the inverse of y =2x^2  is sqrt(x/2)

Answer 2

x=2y2x=2y2

Solve for yy.

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y=√2x2,−√2x2y=2x2,-2x2

Solve for yy and replace with f−1(x)f-1(x).

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f−1(x)=√2x2,−√2x2