# Function and Logic (Math Problem Sample)

Dear student, 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

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.

3.) The function g is related to one of the parent functions

g(x) = −(x − 2)^3

a.) Identify the parent function f.

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

4.) The function g is related to one of the parent functions

g(x) = |x − 1| + 5

a.) Identify the parent function f.

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

5.) The function g is related to one of the parent functions

g(x) = 2 √x

a.) Identify the parent function f.

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

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

### Other Topics:

- Solving Mathematical Problems Involving Graphing and SlopesDescription: * y = 5.5x x 0 1 1 12 2 y 0 5.5 or 5 12 8 14 11 Graph: y x * The slope of the graph is positive. 1 Hours Worked Amount Earned 2 $19.5 3 $29.25 4 $39 2 Use the two points from the graph which are (1, 4 12) and (2, 9). (1, 92) and (2, 9_...1 page/≈550 words| No Sources | MLA | Mathematics & Economics | Math Problem |
- Solving Mathematical Problems Involving TrianglesDescription: In the triangle, cm and cm. Given that the area of the triangle is cm2, find the possible values of the angle. Solution: Using the Area Substitute the given values and simplify. 3654 = 54sinB54 Divide both sides by 54. Therefore, sin B = 23 Angle B = 41.80 or 138.20 Final Answer...1 page/≈550 words| No Sources | MLA | Mathematics & Economics | Math Problem |
- Algebra Task: Simplifying Rational ExpressionDescription: 1 Let P(x) = µx . e-µx! and let µ=10. Find P(9) Solution: P(x) = µx . e-µx! Given. P(x) = 10x . e-10x!Substitute the value of µ=10 from the given. Finding P(9): P(x) = 10x . e-10x!From P(x) using the value of µ=10. P(9) = 109 . e-109!Substitute P(x) to P(9). P(9) = 1099! . e10Rewrite the expression...1 page/≈550 words| No Sources | MLA | Mathematics & Economics | Math Problem |