Finding a new function given a composite function (Case B : Second function is given) Example 1


Example 1 (substitution Method)
A function f is defined by f:xx+2  .
Find the function g if gf:xx2+3x+5  .

[Note : Second function is given, use substitution y = x + 2]



Finding a new function given a composite function (Case A : First function is given) Example 3


Example 3
A function f is defined by f:x2x+1  .
Find the function g if fg:x5x2x+5,x5  .

[Note : First function is given]

Click here (check for example 5)


Finding a new function given a composite function (Case A : First function is given) Example 2


Example 2
A function f is defined by f:x2x .
Find the function g if fg:xx2+1   .

[Note : the first function f is given]

Click here (check for example 5)



Finding a new function given a composite function (Case A : First function is given) Example 1


Example 1
A function f is defined by f:x2x+5  .
Find the function g if fg:x3x8  .

[Note : First function f is given]

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Composite Function (Comparison Method) Example 2


Example 2
Given f:x1x   and g:xpx2+q  .  If the composite function gf  is defined by gf:x3x26x+5  , find
(a) the value of p and of q,
(b) the value of g2(1)  .





Composite Function (Comparison Method) Example 1


Example 1
Given f:xhx+k,g:x(x+1)2+4   and fg:x2(x+1)2+5.  Find
(a) the value of g²(2),
(b) the value of h and of k.







Example 3


Example 3

If f:x2x+1   and g:x5x,x0  .  Find the composite functions gf , fg and the value of gf(4).


Example 2

Given f:x1x and g:xpx2+q. If the composite function gf is defined by gf:x3x26x+5, find

  1. the value of p and of q,
  2. the value of g2(1).

Example 2


Example 2

Functions f and g are defined by f:xx1   and g:x3xx+4  .  Find
(a) the value of gf(3),
(b) the value of fg(-1 ),
(c) the composite functions fg,
(d) the composite functions gf,
(e) the composite functions g²,
(f) the composite functions f².






Example 1

If f : xx + 5 and g : xx2 +2x + 3, find

  1. the value of gf (2),
  2. the value of fg (2 ),
  3. the composite functions fg,
  4. the composite functions gf,
  5. the composite functions g2 ,
  6. the composite functions f2.

correction for part (c)

fg(x)=f(x2+2x+3)=(x2+2x+3)+5=x2+2x+3+5=x2+2x+8