Find the inverse of the function. f(x) = 4x^(2) \\ , x \leq 0 The inverse of g(x) = ___

Question

Find the inverse of the function.

f(x) =
`4x^(2) \\` , x
`\leq` 0

The inverse of g(x) = ___

Answer 1

Explanation:

The inverse is found by interchanging the x and y values and solve the result for y.

I will use y for f(x)

y = 4x^2

Inverse

x = 4y^2 Divide by 4

x/4 = 4y^2 /4

x/4 = y^2 Take the square root of both sides.

sqrt(x/4) = sqrt(y^2)

y = sqrt(x/4)

g(x) = sqrt(x/4) If you have a very fussy teacher, the inverse function could be written as

g(x) = +/- sqrt(x)/2

I expect that if the question is computer marked, I would try g(x) = sqrt(x)/2 first.