The function f and f^2 are defined by f(x)=hx+k and f^2(x)=4x+15 respectively. Considering h>0, how to find the values of x such that f(x^2)=7x ?

Expert Answers
sciencesolve eNotes educator| Certified Educator

The problem provides the information `f^2(x) = 4x + 15 ` and `f(x) = hx + k` , hence, raising `f(x) ` to square should yield `4x + 15` , which is possible only `h = 0` .

Notice that the problem also provides the information that h>0, hence it is impossible for `f^2(x)`  to be `4x + 15`  if `f(x) = hx+k, hgt0.`

Hence, considering the conflicting given informations regarding `f(x), f^2(x)`  and h, it is impossible to solve the equation `f(x^2)=7x.`

wonghoongkok | Student

But h can be determined by using comparison.

Since f(x)=hx+k , then f^2(x)=h(hx+k)+k ~> h^2 x + hk + k . 

By using comparison,

h=2 and k can also be determined. k = 5 

By I don't know how to find the values of x such that f(x^2)=7x ?