Wribreeminsl

2021-02-05

To calculate:To check if $\left(f\ast g\right)\left(x\right)=\left(g\ast f\right)\left(x\right)$. 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 worth 8 points had insufficient data, so nobody could solve that problem.
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student

hosentak

Expert

The function $f\left(x\right)=1$. lxrepresents the score increased by 10%
The function $g\left(x\right)=x+8$ represents the score increased by 8 points
The function $\left(f\ast g\right)\left(x\right)=1.1\left(x+8\right)$ represents the final score when the score is first increased by 8 bonus points and then by 10%
The function $\left(g\ast f\right)\left(x\right)=1.1x+8$ represents the final score when the score is first increased by 10% and then by 8 bonus points

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