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)).

Question

contestada

Respuesta :

frika frika · Answer 1 · 2019-09-24T12:44:26+02:00

Answer:

See explanation

Step-by-step 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,

[tex]f(x)=x+10[/tex]

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

[tex]g(x)=1.09x[/tex]

B. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then

[tex]f(g(x))=g(x)+10=1.09x+10[/tex]

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

[tex]f(g(75))=1.09\cdot 75+10=91.75[/tex]

C. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then

[tex]g(f(x))=1.09f(x)=1.09(x+10)[/tex]

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

[tex]g(f(75))=1.09(75+10)=92.65[/tex]

D. [tex]g(f(x))\neq f(g(x))[/tex] because [tex]1.09(x+10)\neq 1.09x+10[/tex]