Answer:
[tex]f(0) = 14[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \left \{ {{|x - 8| + 6 \ x<4} \atop {15\ x\ge 4}} \right.[/tex]
Required
Find f(0)
From the piecewise function, we have the following as values of f(x):
[tex]f(x) = |x - 8| + 6[/tex]
If [tex]x < 4[/tex]
[tex]f(x) = 15[/tex]
If [tex]x \ge 4\\[/tex]
f(0) implies that [tex]x =0[/tex] and [tex]0<4[/tex]
So, we make use of the first function, which is:
[tex]f(x) = |x - 8| + 6[/tex]
Substitute 0 for x in [tex]f(x) = |x - 8| + 6[/tex]
[tex]f(0) = |0 - 8| + 6[/tex]
[tex]f(0) = |- 8| + 6[/tex]
[tex]|-8| = 8[/tex]
So, the expression becomes
[tex]f(0) = 8 + 6[/tex]
[tex]f(0) = 14[/tex]
Hence, the value of f(0) is 14
