9. Five marks exercise problems III

1. Let \(A =\) \(\{1, 2, 3, 4\}\), \(B = \mathbb{N}\) and \(f : A \rightarrow B\) be defined by \(f(x) = x^3\) then,

 

(i) Find the range of \(f\).

 

\(f = \{\), , , \(\}\)

 

(ii) Identify the type of function.

 

The given function is one-one and onto many-oneone-one and intomany-one and intomany-one and onto  function.

 

 

2. Let \(A = \{-1, 1\}\) and \(B = \{0, 2\}\). If the function \(f : A \rightarrow B\) defined by \(f(x) = ax + b\) is an onto function? Find \(a\) and \(b\).

 

\(a\) \(=\)

 

\(b\) \(=\)

 

 

3. The function '\(t\)' which maps temperature in Celsius (\(C\)) into temperature in Fahrenheit (\(F\)) is defined by \(t(C) = F\) where \(F = \frac{9}{5}C + 32\). Find:

 

(i) \(t(0)\) \(=\) \(^\circ F\)

 

(ii) \(t(28)\) \(=\) \(^\circ F\)

 

(iii) \(t(-10)\) \(=\) \(^\circ F\)

 

(iv) the value of \(C\) when \(t(C) = 212\) \(=\) \(^\circ C\)

 

(v) the temperature when the Celsius values are equal to the Fahrenheit value \(=\) \(^\circ C\)