3 years ago

What is the domain of the absolute value f(x) equals -.5 |X -2|-4

Mathematics

1 answer:

lozanna [386]3 years ago

5 0

Answer:

Domain: All Real Numbers or (-∞, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that any value of <em>x</em> can be plugged into the function.

∴ Our answer is all real numbers

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Naya [18.7K]

let's first off, convert the mixed fractions to improper fractions, and then, let's multiply both sides by the LCD, notice, the LCD will be hmmmm 4, so we'll multiply both sides by 4, to do away with the denominators.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\cfrac{7}{2}w+8=\cfrac{13}{4}w+10\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4\left( \cfrac{7}{2}w+8 \right)=4\left( \cfrac{13}{4}w+10 \right)}
\\\\\\
14w+32=13w+40\implies w=40-32\implies \boxed{w=8}$