Activity: Pure Mathematical Equations (Math Problem Sample)

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