Verified answer

solve x2+6x = 40 --->x = 4 , so g−1(40) = 4

Hello,

g(x) = x² + 6x

x² + 6x = 40

x² + 6x + 9 = 49

(x + 3)² = 7²

(x + 3)² – 7² = 0

(x + 3 – 7)(x + 3 + 7) = 0

(x – 4)(x + 10) = 0

Thus x=4 or x=-10

But since x≥-3 the only possibility is x=4 and

g-1(40) = 4

Regards,

Dragon.Jade :-)

You are trying to find for what x values; x^2+6x=40.

As you factorize x^2+6x, it becomes x(x+6), now try to find x values that makes x(x+6)=40.

x=4 makes 4*10=40, and x=-10 is also (-10)(-4)=40.

However, your range is x>-3 so, (-10) is not in the range, answer is 4.