Question

Let f be a function f : N $\to$ N defined by
f (x) = 3x +2, x $\in$ N. Find the pre-images of 29 and 53.

• A. 9 and 17 respectively
• B. 17 and 9 respectively
• C. -9 and -17 respectively
• D. -17 and -9 respectively

Answer 1

The correct option is A 9 and 17 respectively

Given: The function f : N $\to$ N defined by f (x) = 3x +2, x $\in$ N.
Now, If x is the pre-image of 29, then f (x) = 29 .
Hence, 3x +2 = 29
$\Rightarrow$ 3x = 27
$\Rightarrow$ x = 9

Similarly, if x is the pre-image of 53, then f (x) = 53 .
Hence 3x +2 = 53
$\Rightarrow$3x = 51
$\Rightarrow$ x = 17
Thus the pre-images of 29 and 53 are 9 and 17 respectively.