Daniaal Sanchez

2020-10-27

To calculate:To evaluate .
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 everyones

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The function $f\left(x\right)=1$.larepresents 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 $\left(f\ast g\right)\left(x\right)=1.1x+8$ represents the final score when the score is first increased by 10% and then by 8 bonus points
Calculation:
Consider $\left(f\ast g\right)\left(x\right)=1.1\left(x+8\right)$
Plugging x= 70 in the above equation,
$\left(f\ast g\right)\left(x\right)=1.1\left(70+8\right)=1.1\left(78\right)=85.8$
Consider $\left(g\ast f\right)\left(x\right)=1.1x+8$
Plugging x = 70 in the above equation,
$\left(g\ast f\right)\left(x\right)=1.1\left(70\right)+8=77+8=85$.

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