The function f is defined by f(x) = 2x - 3. If the function g is defined by g(x) = f(x + 4… — SAT

The function $f$ is defined by $f(x) = 2x - 3$ . If the function $g$ is defined by $g(x) = f(x + 4)$ , what is the value of $g(1)$ ?

The correct answer is 7.

Since

g(x) = f(x + 4)

, evaluating

g(1)

requires finding

f(1 + 4)

, which is

f(5)

. Substituting

5

into the expression for

f(x)

gives

f(5) = 2(5) - 3 = 10 - 3 = 7

. Therefore, the correct answer is 7.

Substitute

x = 1

into the definition of

g(x)

to express

g(1)

in terms of

f

g(1) = f(1 + 4) = f(5)

To find the value of

g(1)

, we must evaluate the input to the outer function first.

Substitute the input value

5

into the expression for

f(x)

f(5) = 2(5) - 3

Evaluating

f(5)

requires replacing

x

with

5

in the definition

f(x) = 2x - 3

Perform the operations to find the final value.

f(5) = 10 - 3 = 7

Simplifying the numerical expression gives the final value of

g(1)

Evaluating a transformed function at a given point using function notation.

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