Function and Logic (Math Problem Sample)

SAMPLE
Math & Stat 1 (Calculations)
Task 1: Functions and Relations
Functions and Relations
1
If we double a value X, it’s object will also be doubled and add six to obtain the resultant function:
g(f(x)) = g(x2);
(x2)2 + 6 = x4 + 6
Therefore, g o f = x4 + 6
2
If we double a value of X, we will also double its object and subtract three to obtain the resultant function:
We know that f(x) = x2
g(f(x)) = g(x2)
(x2) 2 – 3 = x4 - 3
Therefore, g o f = x4 – 3
3
*
In order to get f(x), we need to get the inverse of g(x) which we refer it as aour parent function f(x) = g-1
y = (2 – x)3
f(x) = 2 – x3/2
Parent function is given by f(x) = 2 – x3/2
b)
We use original parent function to obtain a child function
g(f(x)) = g (-x3/2 + 2):
(2 – x)3
= (x9/2)
4
a)
For us to get f(x), we need to get the inverse of g(x)and referred it as a parent function
f(x) = g -1
y = |y - 1| +5
x = |y - 1| +5 for y
f(x) = 6 – x or f(x) = x – 4
b)
We use initial function to design a child function
g