Question

if ( f(x)=operatorname{int}(4 x) ), find:
(a) ( f(1.2) ) (b) ( f(2.2) ) (c) ( f(-2.3) )
(a) ( f(1.2)= ) (simplify your answer.)
(b) ( f(2.2)= ) (simplify your answer.)
(c) ( f(-2.3)= ) (simplify your answer.)

Explanation:

Step1: Calculate \(4x\) for each case

For (a) \(x = 1.2\)

\(4x=4\times1.2 = 4.8\)

For (b) \(x = 2.2\)

\(4x=4\times2.2=8.8\)

For (c) \(x=-2.3\)

\(4x=4\times(-2.3)=-9.2\)

Step2: Apply the int function (greatest - integer function)

The int function \(y = \text{int}(t)\) gives the greatest integer less than or equal to \(t\).

For (a) \(t = 4.8\)

\(\text{int}(4.8)=4\) since \(4\leqslant4.8<5\)

For (b) \(t = 8.8\)

\(\text{int}(8.8)=8\) since \(8\leqslant8.8<9\)

For (c) \(t=-9.2\)

\(\text{int}(-9.2)=-10\) since \(- 10\leqslant-9.2<-9\)

Answer:

(a) \(4\)
(b) \(8\)
(c) \(-10\)