write the inverse of f(x) = 4x^2 + 9

Answer 1

To find an inverse, you interchange (i.e., switch) x and y and solve for y.

f(x) = 4x^2 + 9

think of f(x) as y.

y = 4x^2 + 9

Interchange x & y

x = 4y^2 + 9

Solve for y

4y^2 = x-9

y^2= (x-9)/4

y= sqrt((x-9) / 4) or y = - sqrt((x-9) / 4)

include both positive and negative sqrt since either, when squared will yield a positive result.

you can take the square root of 4 to simplify:

y = sqrt(x-9) / 2, -sqrt(x-9)/2

Rewrite using the inverse notation f^-1

f^-1 (x) = sqrt(x-9) / 2 , -sqrt(x-9) / 2

Answer 2

Inverse DNE because f(x) = 4x² + 9 is not one-to-one function: f(- x) = f(x)