Left f(x)=|x| and g(x)=x+2. what are the domain and range of (f°g)(x)

Mathematics

1 answer:

mr_godi [17]3 years ago

5 0

Answer:

$(fog)(x)=|x+2|$

$Dom_{fog} = R$

$Range_{fog}=[0,\infty)$

Step-by-step explanation:

You might be interested in

What expression is equivalent to 1/3(4-5x-1)?

Serhud [2]

1/3( 4 - 5x - 1)

= (1/3)(4 + - 5x + - 1)

= (1/3)( 4) + (1/3)(- 5x) + (1/3)( - 1)

= 4/3 + - 5x/3 + - 1/3

= - 5x/3 + 1 (Decimal: - 1.666667x + 1)

Hope that helps!!!!

3 0

3 years ago

Read 2 more answers

Graph the inverse variation

soldier1979 [14.2K]

X= any coordinate on the x-axis . but I'm confused about the " f "

7 0

4 years ago

I need help with #11

Troyanec [42]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template in mind, let's take a peek at this function

$\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}$

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically

8 0

3 years ago

Read 2 more answers

Los 3/4 de un número es 120. ¿Cuál es el número?

Marina CMI [18]

Maybe...... E if that’s not right then try..... b

5 0

3 years ago

Read 2 more answers

Which expression is equivalent to the following complex fraction?

vladimir2022 [97]

Answer: