Question

6) f(n) = 2n - 5
g(n) = 2n? – 3n - 5
Find f(n)
8(n)

Answer 1

Note: Your question is not clearly explained. But it seems you may have been asking EITHER

Scenario 1:  To find the values of $f(n) = 2n - 5$ and $g\left(n\right)=2n^2-3n-\:5$ when the value of n = 8. So, I am solving based on this scenario.

OR

Scenario 2: To find $\left(f\:\left(g\left(8\right)\right)\right)$ when  $f(n) = 2n - 5$ and $g\left(n\right)=2n^2-3n-\:5$.

So, I solving both scenarios.

Step-by-step explanation:

SOLVING SCENARIO 1

To find the values of $f(n) = 2n - 5$ and $g\left(n\right)=2n^2-3n-\:5$ when the value of n = 8. So, I am solving based on this scenario.

Considering the functions

$f\left(n\right)=2n\:-\:5$

$g\left(n\right)=2n^2-3n-\:5$

Putting n = 8

$f\left(n\right)=2n\:-\:5$

$f\left(8\right)=2\left(8\right)\:-\:5$

$f\left(8\right)=11$

Putting n = 8

$g\left(n\right)=2n^2-3n-\:5$

$g\left(8\right)=2\left(8\right)^2-3\left(8\right)-\:5$

$g\left(8\right)=2\cdot \:8^2-3\cdot \:8-5$

$g\left(8\right)=128-29$

$g\left(8\right)=99$

SOLVING SCENARIO 2

To find $\left(f\:\left(g\left(8\right)\right)\right)$  when  $f(n) = 2n - 5$ and $g\left(n\right)=2n^2-3n-\:5$.

So, I solving both scenarios.

as

$g\left(n\right)=-n^2+5$

$\mathrm{For}\:g=-n^2+5\:\mathrm{substitute}\:n\:\mathrm{with}\:8$

$=-8^2+5$

$=-59$

also

$f(n) = 2n - 5$

$\mathrm{For}\:f=2n+3\:\mathrm{substitute}\:n\:\mathrm{with}\:-59$

$=2\left(-59\right)+3$

so

$2\left(-59\right)+3$

$=-2\cdot \:59+3$

$=-115$

Therefore,

$f=2n+3,\:g=-n^2+5,\:\left(f\:\circ \:\left(g\left(8\right)\right)\right):\quad -115$