Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Inverse equation

1. g(n)= 2+(n+2)^3
2. f(n)= 1/2n+3/2




Sagot :

Answer:

1

[tex]g(n) = 2 + {(n + 2)}^{3} [/tex]

let the inverse be m :

[tex]m = 2 + {(n + 2)}^{3} \\ {(n + 2)}^{3} = m - 2 \\ n + 2 = \sqrt[3]{(m - 2)} \\ n = \{ \sqrt[ 3]{(m - 2)} - 2 \}[/tex]

therefore:

[tex]{ \boxed{ \boxed{g {}^{ - 1}(n) = \{ \sqrt[3]{(n - 2)} - 2 \}}}}[/tex]

2.

[tex]f(n) = \frac{1}{2} n + \frac{3}{2} [/tex]

let inverse be x :

[tex]x = \frac{1}{2} n + \frac{3}{2} \\ \\ 2x = n + 3 \\ n = 2x - 3[/tex]

therefore:

[tex]{ \boxed{ \boxed{f {}^{ - 1}(n) = 2n - 3 }}}[/tex]