Q20 of 26 Page 1

Let be a function defined as Show that is invertible (where S is range of f). Find the inverse of f and hence find and

Given: f(x) = 4x2 + 12x + 15


Let x1, x2 N and f(x1) = f(x2)


From this we can say that


4x12 + 12x1 + 15 = 4x22 + 12x2 + 15


4(x12 - x22) + 12(x1 - x2) = 0


(x1 - x2) (4x1 + 4x2 + 12) = 0


From the above equation it implies that


x1 - x2 = 0


x1 = x2


4x1 + 4x2 + 12 cannot be zero as x1, x2 N


Therefore, f is one to one function


f is also an onto function as its co - domain is equal to the range. As the function is both one to one and onto, f is invertible.


y = 4x2 + 12x + 15


y = (2x + 3)2 + 6


y - 6 = (2x + 3)2


(2x + 3)






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