cl secure l https://www.awhal /alekscgi/x/Isl.exe/lo u-lgNslkr7j8P3jH-IBx4 wheth

Question

cl secure l https://www.awhal /alekscgi/x/Isl.exe/lo u-lgNslkr7j8P3jH-IBx4 whether two functions are Inverses of each other For each pair of functions fand g below, find f(g(x)) and g(f(a)). Then, determine whether fand g are inverses of each other. Simplify. your answers as much as possible. (Assu me that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) (x) 3x (b) f(x) = 2x-3 ao g(x)-3 g(x) =- fand g are inverses of each other o fand g are not inverses of each other f and g are inverses of each other fand g are not inverses of each other Explanation

Explanation / Answer

f(x)=3x, g(x)=x/3

(fog)(x)=f(g(x))=f(x/3) =3(x/3)=x

(gof)(x)=g(f(x))=g(3x)=3x/3=x

Since (fog)(x)=(gof)(x)=x, therefore the functions are inverses of each other.

b. f(x)=2x-3 , g(x)=(x+3)/2

(fog)(x)=f(g(x))=f(x+3/2)=2(x+3/2)-3=x+3-3=x

(gof)(x)=g(f(x))=(2x-3)=(2x-3+3)/2=2x/2=x

Since (fog)(x)=(gof)(x)=x, therefore the functions are inverse of each other.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.