Question let-th
Let the function p be defined as 
, where c is a constant. If 
, what is the value of 
?
10.00
10.25
10.75
11.00
Let the function p be defined as , where c is a constant. If , what
Hard-difficulty · SAT Math · Nonlinear Functions — Function composition and evaluation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. The value of p(12) depends on the value of the constant c, so the value of c must first be determined. It is given that p(c) = 10. Based on the definition of p, it follows that:
This means that 
for all values of x. Therefore:
Choice A is incorrect. It is the value of p(8), not p(12). Choices B and C are incorrect. If one of these values were correct, then x = 12 and the selected value of p(12) could be substituted into the equation to solve for c. However, the values of c that result from choices B and C each result in p(c) < 10.
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