Question

If f(x)=1/x²/³, which of the following is not true?

A) f(1)=1
B) f(8)=/14
C) f(64)=1/8
D) f(27)=1/3

Answer 1

To determine which of the given options is not true for the function f(x) = 1/x²/³, we need to evaluate each option. Based on the calculations, the option that is not true is B) f(8) ≠ 1/4.

Step-by-step explanation:

To determine which of the given options is not true, we need to evaluate each option using the given function f(x) = 1/x²/³.

Let's calculate f(1):

f(1) = 1/(1²/³) = 1/(1³/²) = 1/(1/√1) = 1/1 = 1

So, f(1)=1, which means option A) f(1) = 1 is true.

Now, let's calculate f(8):

f(8) = 1/(8²/³) = 1/(8³/²) = 1/(√8³) = 1/(√512) = 1/√512 ≠ 1/4

So, f(8) ≠ 1/4, which means option B) f(8) ≠ 1/4 is not true.

Similarly, we can calculate f(64) and f(27) to check the remaining options.

f(64) = 1/(64²/³) = 1/(64³/²) = 1/(√64³) = 1/(√262,144) = 1/512 ≠ 1/8

f(27) = 1/(27²/³) = 1/(27³/²) = 1/(√27³) = 1/(√19,683) = 1/243 = 1/3

Therefore, option C) f(64) ≠ 1/8 and option D) f(27) = 1/3 are not true.

Based on the calculations, the option that is not true is B) f(8) ≠ 1/4.