Question

Given f(x) = 2x^2 - 9x + 2, g(x) = 1 - 6x, and h(x) = x^2 - 4, find each fumction. Indicate any restrictions in the domain.

Answer 1

Step-by-step explanation:

Considering the given functions

• $f\left(x\right)\:=\:2x^2\:-\:9x\:+\:2$

• $g\left(x\right)\:=\:1\:-\:6x$

• $h\left(x\right)\:=\:x^2\:-\:4$

As we know that

• the domain is the set of all possible input values of independent variable for which the function is defined.

• And range is the set of all possible output values after the substitution of the values in the domain interval.

• Also note that only real numbers could be included in the domain and range.

There are following two reasons why domains tend to be restricted.

• We can't divided any equation by 0 to prevent the function from becoming undefined.

• We can not take the square root of any negative real number to prevent the function from becoming undefined.

So, lets now check the functions one by one.

FOR THE FUNCTION   $f\left(x\right)\:=\:2x^2\:-\:9x\:+\:2$

Considering the function

• $f\left(x\right)\:=\:2x^2\:-\:9x\:+\:2$

So,

$\mathrm{Domain\:of\:}\:2x^2-9x+2\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

As domain is the set of all real number. Therefore, there are no restrictions in the domain. It means the function is defined for all real numbers.

$\mathrm{Range\:of\:}2x^2-9x+2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-\frac{65}{8}\:\\ \:\mathrm{Interval\:Notation:}&\:[-\frac{65}{8},\:\infty \:)\end{bmatrix}$

The graph is also shown. The green color Parabola is the graph of the function $f\left(x\right)\:=\:2x^2\:-\:9x\:+\:2$.

FOR THE FUNCTION $g\left(x\right)\:=\:1\:-\:6x$

Considering the function

• $g\left(x\right)\:=\:1\:-\:6x$

As

$\mathrm{Domain\:of\:}\:1-6x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

As domain is the set of all real number. Therefore, there are no restrictions in the domain. It means the function is defined for all real numbers.

$\mathrm{Range\:of\:}1-6x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

The graph is also shown. The blue color straight line is the graph of the function $g\left(x\right)\:=\:1\:-\:6x$.

FOR THE FUNCTION  $h\left(x\right)\:=\:x^2\:-\:4$

Considering the function

• $h\left(x\right)\:=\:x^2\:-\:4$

As

$\mathrm{Domain\:of\:}\:x^2-4\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

As domain is the set of all real number. Therefore, there are no restrictions in the domain. It means the function is defined for all real numbers.

$\mathrm{Range\:of\:}x^2-4:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}$

The graph is also shown. The black color parabola is the graph of the function $h\left(x\right)\:=\:x^2\:-\:4$.

Keywords: equation, graph, function, domain, range, restricted values

Learn more about function and graph from brainly.com/question/14013504

#learnwithBrainly

Answer 2

Answer:

Is this for the 5.7 function and composition of function worksheet ? I have the answers text my number 8138432311 and I’ll give you all of it

Step-by-step explanation: