BackClose

Select a Subject

Subject Test Math 2

Question 25 of 28

beginning of content:
Tags:
SAT Subject Test

If f left parenthesis x right parenthesis equals root index 3 of x to the power of 3 end exponent plus 1 end root, what is f to the power of negative 1 end exponent left parenthesis 1.5 right parenthesis?

Select an Answer

3.4

Correct Answer: 
No

2.4

Correct Answer: 
No

1.6

Correct Answer: 
No

1.5

Correct Answer: 
No

1.3

Correct Answer: 
Yes

The correct answer is E.

One way to determine the value of f to the power of negative 1 end exponent left parenthesis 1.5 right parenthesis is to solve the equation f left parenthesis x right parenthesis equals 1.5 for x. Since f left parenthesis x right parenthesis equals root index 3 of x to the power of 3 end exponent plus 1 end root, start with the equation root index 3 of x to the power of 3 end exponent plus 1 end root equals 1.5, and cube both sides to get x to the power of 3 end exponent plus 1 equals left parenthesis 1.5 right parenthesis to the power of 3 end exponent equals 3.375. Isolate x to get x to the power of 3 end exponent equals 2.375, and apply the cube root to both sides of the equation to get x equals root index 3 of 2.375 end root almost equal to 1.3.

Another way to determine the value of f to the power of negative 1 end exponent left parenthesis 1.5 right parenthesis is to find a formula for f to the power of negative 1 end exponent and then evaluate at 1.5. Let y equals root index 3 of x to the power of 3 end exponent plus 1 end root and solve for x: cubing both sides gives y to the power of 3 end exponent equals x to the power of 3 end exponent plus 1, so x to the power of 3 end exponent equals y to the power of 3 end exponent minus 1, and x equals root index 3 of y to the power of 3 end exponent minus 1 end root.  Therefore, f to the power of negative 1 end exponent left parenthesis y right parenthesis equals root index 3 of y to the power of 3 end exponent minus 1 end root, and f to the power of negative 1 end exponent left parenthesis 1.5 right parenthesis equals root index 3 of left parenthesis 1.5 right parenthesis to the power of 3 end exponent minus 1 end root equals root index 3 of 2.375 end root almost equal to 1.3.

Question Difficulty: 
hard