Question

Suppose your teacher offers to give the whole class a bonus if everyone passes the next math test. The teacher

says she will 1)give a 10-point bonus and (2) increase everyone's grade by 9% of their score. a. Let x represent the original test scores.Write statements (1) and (2) as the functions f (x) and g(x) respectively.b. Explain the meaning of f(g(x)). Evaluate f(g(75)).c. Explain the meaning of g (f(x)). Evaluate g (f(75)). d. Does g(f(x))=f(g(x)).​

Answer 1

See explanation

Explanation:

A. Let x represent the original test scores.

(1) The teacher will give a 10-point bonus, then the score will be x + 10. Hence,

`f(x)=x+10`

(2) The teacher will increase everyone's grade by 9% of their score, then the score will be x + 0.09x = 1.09x. Hence,

`g(x)=1.09x`

B. If
`f(x)=x+10` and
`g(x)=1.09x,` then

`f(g(x))=g(x)+10=1.09x+10`

Meaning: the teacher increased by 9% the score and then increased the result by 10 points.

`f(g(75))=1.09\cdot 75+10=91.75`

C. If
`f(x)=x+10` and
`g(x)=1.09x,` then

`g(f(x))=1.09f(x)=1.09(x+10)`

Meaning: the teacher increased by 10 points the score and then increased the result by 9%.

`g(f(75))=1.09(75+10)=92.65`

D.
`g(f(x))\\eq f(g(x))` because
`1.09(x+10)\\eq 1.09x+10`