For the function f, it is given that f(4) = 18. The function g is defined by g(x) = \frac{… — SAT

For the function $f$ , it is given that $f(4) = 18$ . The function $g$ is defined by $g(x) = \frac{1}{3}f(x + 2)$ . What is the value of $g(2)$ ?

Answer: 6

The value of

g(2)

is 6.

To evaluate

g(2)

, substitute

x = 2

into the definition

g(x) = \frac{1}{3}f(x+2)

, which yields

g(2) = \frac{1}{3}f(2+2) = \frac{1}{3}f(4)

. Since

f(4) = 18

, this simplifies to

\frac{1}{3}(18) = 6

Substitute

x = 2

into the expression for

g(x)

g(2) = \frac{1}{3}f(2 + 2)

To evaluate the function

g

x = 2

, we substitute 2 for every occurrence of

x

in the function definition.

Simplify the input argument for the function

f

g(2) = \frac{1}{3}f(4)

Adding 2 and 2 inside the parentheses simplifies the input of

f

to 4.

Substitute the given value of

f(4)

into the simplified expression.

g(2) = \frac{1}{3}(18)

The problem states that

f(4) = 18

Perform the final multiplication.

Multiplying 18 by

\frac{1}{3}

is equivalent to dividing 18 by 3, which yields 6.

Evaluating a transformed function by substituting a value into function notation.

Estimated Time:45s

Question