For all real numbers x, the function g is defined by g(x) = 5 - 2x^2. What is the value of… — GRE General Test

For all real numbers $x$ , the function $g$ is defined by $g(x) = 5 - 2x^2$ . What is the value of $g(g(2))$ ?

-13

Evaluating the inner expression

g(2)

gives

5 - 2(2)^2 = 5 - 8 = -3

. Substituting

-3

back into the function

g(x)

gives

g(-3) = 5 - 2(-3)^2 = 5 - 2(9) = -13

. Thus, the correct value is

-13

Evaluate the inner function

g(2)

g(2) = 5 - 2(2)^2 = 5 - 2(4) = 5 - 8 = -3

Substitute

x = 2

into the definition of

g(x)

and follow standard order of operations (exponents before multiplication).

Substitute the result into the outer function to evaluate

g(-3)

g(-3) = 5 - 2(-3)^2 = 5 - 2(9) = 5 - 18 = -13

Squaring a negative number yields a positive result, so

(-3)^2 = 9

, which is then multiplied by

2

Nested Function Evaluation and Order of Operations

Estimated Time:45s

Question