Math 123 Essay
Math is a subject that involves the science of numbers and their operations, interrelations, combinations, generalizations, abstractions and of space configurations and their structure, measurement, transformations, and generalizations (Merriam- Webster, 2013). Depending on the person, math can be an easy or challenging subject to conquer. Not everyone can solve math problems with little to no effort involved. Students are often given exams to test their knowledge of the subject. In Professor Hoffman’s Pre-Calculus class, we were given a test that covered sections 1.1-1.5 in our text book. There were a total of two parts to this test. Part one was the “no calculator test” and part two was the “calculator test”. On the “calculator test” I answered question number ten incorrectly. In this essay I will demonstrate how I corrected number ten so I can better understand what went wrong. I will also explain what went wrong during my thinking process during the test and how I came up with my solution.
To help better understand the question we must look at what the problem is telling us. Number ten states the following: Given f(x) = 2x2 – 5 and g(x) = 4 – x, find A. (f o g)(x) and B. (g o f)(x). In other words, letter A. is asking: solve for x when you plug g(x) in place of f(x) and letter B. is asking: solve for x when you plug f(x) in place of g(x). First, lets’ look at letter A., and how we can set the problem up. Since the problem is asking us to find g of f of x, we have to plug in g(x) for f(x). We can write letter A. as f(g(x)) = 2(4-x) 2 – 5. We must look at what we already know from having previous experience in this subject. We know that (4-x)2 can be factored out to (4-x)(4-x), so the new problem would look like this: 2(4 – x)(4 – x) – 5. We also know that the (4 – x)(4 – x) in the new equation can also be foiled to make the next couple of steps easier. “FOIL” consist of multiplying the two, two term polynomials together by the first terms, the outer
To help better understand the question we must look at what the problem is telling us. Number ten states the following: Given f(x) = 2x2 – 5 and g(x) = 4 – x, find A. (f o g)(x) and B. (g o f)(x). In other words, letter A. is asking: solve for x when you plug g(x) in place of f(x) and letter B. is asking: solve for x when you plug f(x) in place of g(x). First, lets’ look at letter A., and how we can set the problem up. Since the problem is asking us to find g of f of x, we have to plug in g(x) for f(x). We can write letter A. as f(g(x)) = 2(4-x) 2 – 5. We must look at what we already know from having previous experience in this subject. We know that (4-x)2 can be factored out to (4-x)(4-x), so the new problem would look like this: 2(4 – x)(4 – x) – 5. We also know that the (4 – x)(4 – x) in the new equation can also be foiled to make the next couple of steps easier. “FOIL” consist of multiplying the two, two term polynomials together by the first terms, the outer
References: Merriam- Webster, (2013). Mathematics. Retrieved from http://www.merriam-webster.com/dictionary/mathematics