Composition and Inverse of Functions

Composition and Inverse of Functions

Functions are applied in real life scenarios in many different applications and in various work fields. One of these work fields is physics and astronomy. They use functions to calculate various studies on the trajectory of stars, planets and asteroids out in space. Einstein used the E=mc2 function to show the physical mass or fluid of an object and how much force it would take to move said mass at the speed of light. These fields have allowed us to understand our natural world around us and our place within the world.

In this final assignment, I have been given these functions to work with to combine, compose and to find the inverses of certain functions. These are the functions as they follow:

fx=2x+5 gx=x2-3 hx=7-x3

I need to compute (f-h)(4) for this assignment:

f-h4=f4-h(4) I need to evaluate f and h separately and then subtract from each other to solve this problem.

f4=24+5 The first function to be evaluated with all values plugged in.

f4=8+5=13 f4=13

h4=(7-4)3 The second function to be evaluated with all the values plugged in it.

h4=33=1 h4=1

f-h4=13-1=12 This is my final answer

Next, I am to compose two pairs of functions into each other. First, I will work out

f ° gx=f(gx) This means that the rule of f will work on g.

=f(x2-3) Here f is going to work on the rule of g.

=2x2-3+5 The rule of f is applied to g.

=2x2-6+5 Now I need to simplify the problem

f ° gx=2x2-1 My final results.

Now I will compose the following pair of functions into each other:

h ° gx=h(gx) The rule of h will work on g.

=h(x2-3) Here h is going to work on the rule of g.

=7-(x2-3)3 The rule of h is applied to g.

h ° gx=4-x23 My final answer.

For the next part of this assignment, I am asked to transform g(x), so that the graph is placed six units to the right and seven units downwards from where it would be right now.

* Six units to the right means that I will be placing the -6 in with the x...