Answer:
Option 2nd is correct.
[tex]f[g(6)][/tex] =0.
Step-by-step explanation:
Given the function:
[tex]f(x) = 6x+12[/tex]
[tex]g(x) = x-8[/tex]
Solve: [tex]f[g(6)][/tex]
First calculate:
f[g(x)]
Substitute the function g(x)
[tex]f[x-8][/tex]
Replace x with x-8 in the function f(x) we get;
[tex]f(x-8) = 6(x-8)+12[/tex]
The distributive property says that:
[tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
Using distributive property:
[tex]f(x-8) = 6x-48+12 = 6x-36[/tex]
⇒[tex]f[g(x)] = 6x-36[/tex]
Put x = 6 we get;
[tex]f[g(6)] = 6(6)-36 = 36-36 =0[/tex]
Therefore, the value of [tex]f[g(6)][/tex] is 0.
