Answer:
[tex]g(f(2))=3[/tex]
Step-by-step explanation:
So we have:
[tex]f(x)=4x-3\text{ and } g(x)=\frac{2x-1}{3}[/tex]
And we want to solve for g(f(2)).
First, find f(2):
[tex]f(2)=4(2)-3[/tex]
Multiply:
[tex]f(2)=8-3[/tex]
Subtract:
[tex]f(2)=5[/tex]
Now, substitute this in for g(f(2)):
[tex]g(f(2))=g(5)[/tex]
Substitute this in for g(x):
[tex]g(5)=\frac{2(5)-1}{3}[/tex]
Multiply:
[tex]g(5)=\frac{10-1}{3}[/tex]
Subtract:
[tex]g(5)=\frac{9}{3}[/tex]
Divide:
[tex]g(5)=3[/tex]
Therefore:
[tex]g(f(2))=3[/tex]
