Answer:
Option D is correct.
[tex]f[g(10)][/tex] = 198
Step-by-step explanation:
Given the function:
[tex]f(x) = 10x+8[/tex]
[tex]g(x) = x+9[/tex]
Solve: [tex]f[g(10)][/tex]
First calculate:
f[g(x)]
Substitute the function g(x)
[tex]f[x+9][/tex]
Replace x with x+9 in the function f(x) we get;
[tex]f(x+9) = 10(x+9)+8[/tex]
The distributive property says that:
[tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
Using distributive property:
[tex]f(x+9) = 10x+90+8=10x+98[/tex]
⇒[tex]f[g(x)] = 10x+98[/tex]
Put x = 10 we get;
[tex]f[g(10)] =10(10)+98=100+98=198 [/tex]
Therefore, the value of [tex]f[g(10)][/tex] is 198
