6. Five marks example problems II

1. Let \(f\) be a function \(f: \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(x) = 3x + 2\), \(x \in \mathbb{N}\).

 

(i) Find the images of \(1\), \(2\), \(3\).

 

 

(ii) Find the pre-images of \(29\), \(53\).

 

 

(iii) Identify the type of function.

 

 

2. Forensic scientists can determine the height (in cms) of a person based on the length of their thigh bones. They usually use the function \(h(b) = 2.47b + 54.10\) where \(b\) is the thigh bone length.

 

(i) Check if the function \(h\) is one-to-one.

 

 

(ii) Also find the height of a person if the length of his thigh bone is \(50\) \(cms\).

 

\(cms\).

 

(iii) Find the length of the thigh bone if the height of a person is \(147.96\) \(cms\).

 

 \(cms\).

 

 

3. The distance \(S\) (in kms) travelled by a particle in time '\(t\)' hours is given by \(S(t) = \frac{t^2 + t}{2}\). Find the distance travelled by the particle after

 

(i) three and half hours.

 

 \(kms\).

 

(ii) eight hours and fifteen minutes.

 

 \(kms\).

 

[Note: Round off your answer to three decimal places.]