**Example 3:**

Given

*f*:*x*→*hx*+*k*and*f*^{2}:*x*→ 4*x*+ 15. (a) Find the values of

*h*and of*k*. (b) Take

*h*> 0, find the values of*x*for which*f*(*x*^{2}) = 7*x*

*Solution:***(a)**

**Step 1:**find

*f*

^{2}(

*x*)

Given

*f*(*x*) =*hx*+*k**f*

^{2}(

*x*) =

*ff*(

*x*) =

*f*(

*hx*+

*k*)

=

*h*(*hx*+*k*) +*k* =

*h*^{2}*x*+*hk*+*k***Step 2:**compare with given

*f*

^{2}(

*x*)

*f*

^{2}(

*x*) = 4

*x*+ 15

*h*

^{2}

*x*+

*hk*+

*k*= 4

*x*+ 15

*h*

^{2 }= 4

*h*= ± 2

When,

*h*= 2*hk*+

*k*= 15

2

*k*+*k*= 15*k*= 5

When,

*h*= –2*hk*+

*k*= 15

–2

*k*+*k*= 15*k*= –15

**(b)**

*h*> 0,

*h*= 2,

*k*= 5

Given

*f*(*x*) =*hx*+*k**f*(

*x*) = 2

*x*+ 5

*f*(

*x*

^{2}) = 7

*x*

2 (

*x*^{2}) + 5 = 7*x*2

*x*^{2}– 7*x*+ 5 = 0(2

*x*– 5)(*x*–1) = 02

*x*– 5 = 0 or*x*–1= 0

*x***= 5/2**

*x***= 1**