The figure above shows the representations of… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

The figure above shows the representations of the graphs of the functions f and g, where $f(x) = 2^{-0.5x}$ and $g(x) = ax^2+b$ (a and b constants). What is the value of $g(f(0))$ ?

Answer Choices

Correct answer marked below

3.25

3.5

3.75

Correct

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Explanation

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Official Explanation

Official

We need to find

g(f(0))

.

First, evaluate

f(0)

f(0) = 2^{-\frac{1}{2}(0)} = 2^0 = 1

.

Thus,

g(f(0)) = g(1) = a \cdot 1^2 + b = a + b

.

Now determine constants

a

and

b

from the graphs.

From the blue graph (f), the point

(-4, b)

lies on it, so:

b = 2^{-\frac{1}{2}(-4)} = 2^{2} = 4

.…

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What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

The figure above shows the representations of the graphs of the functions f and g, where f(x)=2−0.5xf(x) = 2^{-0.5x}f(x)=2−0.5x and g(x)=ax2+bg(x) = ax^2+bg(x)=ax2+b (a and b constants). What is the value of g(f(0))g(f(0))g(f(0))?