Question:
The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0 4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
Answer:
The values are [tex]$f(-3)=-8$[/tex] and [tex]$f(2)=8$[/tex]
Explanation:
The function is defined by two parts,
[tex]$f(x)=3 x+1$[/tex] if [tex]x\leq 0[/tex]
[tex]f(x)=2x^2[/tex] if [tex]$x \geq 2$[/tex]
To determine the value of [tex]$f(-3)[/tex] , we shall substitute the value [tex]x=-3[/tex] in the function [tex]$f(x)=3 x+1$[/tex] because [tex]$-3 \leq 0$[/tex]
Hence, we have,
[tex]f(x) \ \ =3 x+1\\f(-3)=3(-3)+1\\f(-3)=-9+1\\f(-3)=-8[/tex]
Now, to determine the value of [tex]f(2)[/tex] , we shall substitute the value [tex]x=2[/tex] in the function [tex]f(x)=2x^2[/tex] because [tex]$x \geq 2$[/tex]
Hence, we have,
[tex]f(x)=2 x^{2}\\f(2)=2\left(2^{2}\right)\\f(2)=2(4)\\f(2)=8[/tex]
Thus, the values are [tex]$f(-3)=-8$[/tex] and [tex]$f(2)=8$[/tex]
