Answer:
Option c is correct.
the value of g(f(1)) is, 4
Step-by-step explanation:
Given the functions:
[tex]f(x) = 6x+2[/tex]
[tex]g(x) = \frac{2x+4}{5}[/tex]
We have to find the g(f(1):
[tex]g(f(x)) = g(6x+2)[/tex]
Substitute 6x+2 in place of x in the function g(x) we have;
[tex]g(f(x)) = g(6x+2) = \frac{2(6x+2)+4}{5}[/tex]
⇒[tex]g(f(x)) = \frac{12x+4+4}{5} = \frac{12x+8}{5}[/tex]
Substitute x = 1 we have;
[tex]g(f(1)) = \frac{12(1)+8}{5} = \frac{12+8}{5} = \frac{20}{5}=4[/tex]
Therefore, the value of g(f(1)) is, 4
