+647 Suppose g(x)=4x^2+8x+13. Does g have an inverse? If so, find g^{-1}(25). If not, enter "undef".
+129850 Not a strict inverse, since it's not one-to-one
However.....it we restict the domain to [-1, inf ) we have
y = 4x^2 + 8x + 13
y - 13 + 4 = 4[ x^2 + 2x + 1]
y - 9 = 4 ( x + 1)^2
[ y - 9] / 4 = (x + 1)^2
√ [ (y - 9) / 4 ] = x + 1
√ [ (y - 9) / 4 ] - 1 = x swap x and y and for y write f-1 (x)
√ [ (x - 9) / 4 ] - 1 = y = f-1 (x)
So f-1 (25 ) = √ [ (25 - 9) / 4 ] - 1 = √ [ 16 / 4 ] - 1 = √4 - 1 = 2 - 1 = 1
