Answer:
[tex]\boxed {\boxed {\sf f(g(0))= 1}}[/tex]
Step-by-step explanation:
We are asked to find the value of f(g(0)). We must start from the inside with g(0).
1. g(0)
The function is: g(x)= 2x-1. We want to find g(0), so we must substitute 0 in for x.
[tex]g(0)=2(0)-1[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Multiply 2 and 0.
[tex]g(0)= 0-1[/tex]
Subtract.
[tex]g(0)= -1[/tex]
2. f(-1)
Since g(0) is equal to -1, f(g(0)) is equal to f(-1). The function is f(x)= x²+4x+4. We want to find f(-1), so we must substitute -1 in for x.
[tex]f(-1)= (-1)^2+4(-1)+4[/tex]
Solve according to PEMDAS. Solve the exponent first.
[tex]f(-1)= 1+4(-1)+4[/tex]
Multiply.
[tex]f(-1)= 1-4+4[/tex]
Subtract, then add.
[tex]f(-1)=-3+4 = 1[/tex]
f(g(0)) is equal to 1.
