Question

I don’t know how to solve this please help me solve B please!

Answer 1

Given

$f(x)=\begin{cases}8x-8{\text{ if x }<\text{ 0}} \\ {-8x-16\text{ if x}\ge0}\end{cases}$

Find

b) f(0) ,

c) f(2) ,

d) exact value of x such that f(x) = -26

e) domain of function

Explanation

b) f(0)

$f(0)=-8(0)-16=-16$

c) f(2)

$f(2)=-8(2)-1=32$

d) f(x)=-26

$\begin{gathered} 8x-8=-26 \\ 8x=-26+8 \\ 8x=-18 \\ x=-2.25 \end{gathered}$

and

$\begin{gathered} -8x-16=-26 \\ -8x=-26+16 \\ -8x=-10 \\ x=1.25 \end{gathered}$

f(x) = -8x-8 and f(x)=-8x-16 is valid for all values of x

So the domain of the function is

$Domain=(-\infty,\infty)$

Final Answer

b) f(0) = -16,

c) f(2) = 32,

d) exact value of x such that f(x) = -26, = -2.25, 1.25

e) domain of function

$Domain=(-\infty,\infty)$