Question

Given f(x)=x² and g(x)=[x/2], select the correct value for fog (-3/2).

1) Cannot be determined
2) 1/4
3) 9/4
4) 3/2

Answer 1

The correct value for fog(-3/2) is 3/2. Option D is answer.

Step-by-step explanation:

Function composition:

We are asked to find the value of fog(-3/2). This means we need to apply the function g to the output of the function f(-3/2).

Calculating f(-3/2):

f(x) = x², so f(-3/2) = (-3/2)² = 9/4.

Calculating g(9/4):

g(x) = [x/2], which means it takes the integer part of the number. Therefore, g(9/4) = [9/2] = 4.

Final result:

Therefore, fog(-3/2) = g(f(-3/2)) = g(9/4) = 4.

Note: The other options are incorrect because:

1/4: This value is obtained by calculating g(-3/2) directly, not by applying g to the output of f(-3/2).

9/4: This value is the output of f(-3/2), not fog(-3/2).

Cannot be determined: There is sufficient information to determine the value of fog(-3/2).

Option D is answer.