Professor Harsh gave a test to his college algebra class, and nobody got more th

Question

Professor Harsh gave a test to his college algebra class, and nobody got more than 80 points (out of 100) on the test. One problem is worth 8 points had insufficient data, so nobody could solve that problem. The professor adjusts the grades for the class by (1) increasing everyone's score by 10% and (2) giving everyone 8 bonus points. Let x represent the original score of a student. Write statements (1) and (2) as functions f(x) and g(x), respectively. Find (f degree g)(x) and explain what it means. Find (g degree f)(x) and explain what it means. Evaluate (f degree g)(70) and (g degree f)(70). Does (f degree g)(x) = (g degree f)(x)? Suppose a score of 90 or better qualifies a student to receive an A on the test. What original score will qualify a student to receive an A on the test if the professor used (i) (f degree g)(x); (ii) (g degree f)(x)?

Explanation / Answer

Here x is the original marks

And for part a, scores increased by 10%

That is f(x)=x+.1x=1.1x

And for part b, 8 bonus points are given

That is g(x)=x+8

B. fog(x)=f(g(x))=f(x+8) = 1.1(x+8)

fog (x) represents 10% extra marks are given on the marks obtained by adding 8 bonus marks

C. gof(x)=g(f(x)) = g(1.1x) = 1.1x+8

gof(x) represents 8 bonus marks are added on the marks obtained by increasing marks by 10%

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