Given:
[tex]f(x)=\begin{cases}{x^2}\text{ .............If }x<0 \\ {-1\text{ ............If }x=0} \\ {3x+4....\text{ If }x>0}\end{cases}[/tex]Find-:
[tex]\begin{gathered} (a)f(-2) \\ \\ (b)f(0) \\ \\ (c)f(1) \end{gathered}[/tex]Sol:
(a)
At f(-2) the value of x is less then zero (0) then function apply is:
[tex]\begin{gathered} f(x)=x^2 \\ \text{ at }x<0 \end{gathered}[/tex]So the value is:
[tex]\begin{gathered} f(x)=x^2 \\ \\ f(-2)=(-2)^2 \\ \\ f(-2)=4 \end{gathered}[/tex](b)
At f(0) the value of x is zero (0) then function value at x = 0 is:
[tex]\begin{gathered} f(x)=-1 \\ \text{ at }x=0 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} f(x)=-1 \\ f(0)=-1 \end{gathered}[/tex](c)
At f(1) then the value of x is 1 so the function apply is:
[tex]\begin{gathered} f(x)=3x+4 \\ \\ \text{ At }x>0 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} f(x)=3x+4 \\ \\ f(1)=3(1)+4 \\ \\ f(1)=3+4 \\ \\ f(1)=7 \end{gathered}[/tex]