Finding a new function given a composite function (Case B : Second function is given) Example 3

Posted on April 18, 2020 by user

Example 3 (Substitution Method)
A function f is defined by

f : x \mapsto \frac{7}{x}

.
Find the function g if

g f : x \mapsto \frac{10}{2 x + 3}, x \neq - \frac{3}{2}

.

[Note : Second function is given, use substitution method]

Finding a new function given a composite function (Case B : Second function is given) Example 2

Posted on April 18, 2020 by user

Example 2 (Substitution Method)
A function f is defined by

f : x \mapsto x - 1

.
Find the function g if

g f : x \mapsto \frac{4}{x + 2}, x \neq - 2

.

[Note : Second function is given , use substitution y = x - 1]

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

Posted on April 18, 2020 by user

Example 1 (substitution Method)
A function f is defined by

f : x \mapsto x + 2

.
Find the function g if

g f : x \mapsto x^{2} + 3 x + 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

Posted on April 18, 2020 by user

Example 3
A function f is defined by

f : x \mapsto 2 x + 1

.
Find the function g if

f g : x \mapsto \frac{5 x - 2}{x + 5}, x \neq - 5

.

[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

Posted on April 18, 2020 by user

Example 2
A function f is defined by

f : x \mapsto \frac{2}{x}

.
Find the function g if

f g : x \mapsto x^{2} + 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

Posted on April 18, 2020 by user

Example 1
A function f is defined by

f : x \mapsto 2 x + 5

.
Find the function g if

f g : x \mapsto 3 x - 8

.

[Note : First function f is given]

Click here (check for example 5) to learn more about function

Composite Function (Comparison Method) Example 2

Posted on April 18, 2020 by user

Example 2
Given

f : x \mapsto 1 - x

and

g : x \mapsto p x^{2} + q

. If the composite function gf is defined by

g f : x \mapsto 3 x^{2} - 6 x + 5

, find
(a) the value of p and of q,
(b) the value of

g^{2} (- 1)

Composite Function (Comparison Method) Example 1

Posted on April 18, 2020 by user

Example 1
Given

f : x \mapsto h x + k, g : x \mapsto {(x + 1)}^{2} + 4

and

f g : x \mapsto 2 {(x + 1)}^{2} + 5.

Find
(a) the value of g²(2),
(b) the value of h and of k.

Example 3

Posted on April 18, 2020 by user

Example 3

If

f : x \mapsto 2 x + 1

and

g : x \mapsto \frac{5}{x}, x \neq 0

. Find the composite functions gf , fg and the value of gf(4).

Example 2

Posted on April 18, 2020 by user

Given $f : x \mapsto 1 - x$ and $g : x \mapsto p x^{2} + q$ . If the composite function gf is defined by $g f : x \mapsto 3 x^{2} - 6 x + 5$ , find

the value of p and of q,
the value of $g^{2} (- 1)$ .