Question

Match the following questions with their answer given the following equations.

a) g(1)
b) f(-2)
c) 2f(5) - 3g(2)
d) No matching question.

Equation 1: f(x) = 20
Equation 2: g(x) = x^2 + 2

Which question matches Equation 2?
a) 2x^2 + 2
b) 18
c) 20
d) 1

Answer 1

The question matching Equation 2, which is g(x) = x^2 + 2, is b) 18 since this output can be achieved by substituting x = 4 into the function g(x).

Step-by-step explanation:

The question asks us to match a question with its corresponding answer given the equation g(x) = x^2 + 2. Equation 2 is a quadratic equation because it involves the square of the variable x (x^2). The options provided correspond to the potential outputs of this function.

To find the answer that matches this equation, we evaluate g(x) at different inputs. Let's look at each option:

• a) 2x^2 + 2: This represents a function, not an output for a specific value of x.
• b) 18: If we find an x such that g(x) = 18, we solve x^2 + 2 = 18, which gives x^2 = 16, so x = ±4. Thus, this could be an output from g(x).
• c) 20: Similarly, if g(x) = 20, we solve x^2 + 2 = 20, which gives x^2 = 18, but since √18 is not a whole number, it's unlikely this output matches the equation as directly as option b.
• d) 1: If g(x) = 1, we solve x^2 + 2 = 1, which is not possible since the minimum value of x^2 + 2 is when x = 0, and it equals 2.

Therefore, the correct answer is b) 18, as it is the only number that can be directly calculated from the function g(x) by inputting the value x = 4.