Composition and Inverse

Composition and Inverse
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MATH 222 Week 5 Assignment
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Composition and Inverse

This week assignment was to understand and solve for composition and inversion. With the given problems and functions I will demonstrate how to compute a problem using composition. Then finally I will demonstrate how to solve a function using inversion.

I will define the following functions to solve the problem. f(x)+2x+5 g(x)=x^2-3 h(x)=7-x ______ 3
The first step is to compute the required problem (f-h)(4).
(f-h)(4)
f(4)-h(4) The first step is to multiply 4 into f and h to be subtracted from each other. Since the equation require functions f and h, we will plug them into the problem.

f(4)-h(4)= [2(4)+5]-[7-(4)] _____ [3] Solve for functions f and h while substituting the x for the number 4

=13 - 11 ___ 3 Subtract

= 28 ___ 3 Final answer
The next step is to evaluate the following compositions.
A: (f o g)(x)= 2(x^2-3)+5 Multiply 2 to the equation in the parenthesis = 2x^2-6+5 Sutract -6 from 5 = 2x^2-1 Final answer

B: (h o g)(x)= 7-(x^2-3) ________ 7 =-x^2+3

Next you have to graph and transform the g(x) function by moving to the right 6 and down 7. g(x)= x^2-3 = (x-6)^2-3-7 Since it is moving -6 right and -7 down would plug the corresponding numbers in to the equation and solve

= (x-6)^2-10 Final solution

Finally, the following functions will be solved using inversion.

C. f(x)= 2x+5 x=2x+5 x=2y+5 replace 2x with 2y x-5=2y subtract 5 from both sides

References: Dugopolski, M. (2012. Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.