Question

For the following functions for f(x) and g(x), find the value of f(g(0)).

f(x) = x² + 4x + 4 and g(x) = 2x - 1

Answer 1

`\boxed {\boxed {\sf f(g(0))= 1}}`

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.

`g(0)=2(0)-1`

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Multiply 2 and 0.

`g(0)= 0-1`

Subtract.

`g(0)= -1`

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.

`f(-1)= (-1)^2+4(-1)+4`

Solve according to PEMDAS. Solve the exponent first.

• (-1)²= -1*-1= 1

`f(-1)= 1+4(-1)+4`

Multiply.

`f(-1)= 1-4+4`

Subtract, then add.

`f(-1)=-3+4 = 1`

f(g(0)) is equal to 1.