# Activity: Pure Mathematical Equations (Math Problem Sample)

Solving for Parent functions in a composite problem

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Student’s Name

Professor’s Name

Subject

Date

Task 1

Overview:

Dear writer, you are to provide solutions for the following problems:

1.)

The function g is related to one of the parent functions

g(x) = x^2 + 6

The parent function f is:

f(x)= x^2

Solution

We Say Whenever we double a value X, we will double it’s object and add six to it to get the resultant function:

g(f(x)) = g(x^2);

(x^2)^2 + 6 = x^4 +6

Say g o f = x^4 +6

Use function notation to write g in terms of f.

2.)

The function g is related to one of the parent functions

g(x) = x2 – 3

The parent function is:

f(x)= x^2

Use function notation to write g in terms of f.

Solution

We Say Whenever we double a value X, we will double its object and subtract three it to get the resultant function:

We know that f(x) = x^2

g(f(x)) = g (x^2)

(x^2)^2-3

Hence

g o f = x^4 - 3

3.)

The function g is related to one of the parent functions

g(x) = −(x − 2)^3

a.) Identify the parent function f.

Solution

For us to get f(x) we get the inverse of g(x) and referred it as our parent function

f(x) = g^(-1)

y= (2-x)^3

f(x) = 2-x^3/2

b.) Use function notation to write g in terms of f

Solution

We Use initial parent function to design a child function

g(f(x)) = g (-x ^3/2 + 2) :

(2-x) ^ 3

(x^9/2)

4.)

The function g is related to one of the parent functions

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