Mathematics: Need some with my last problem for the night. determine the domain of tbe function (f o g)(x) where f(x) = 3x-1/x-4 and g(x) = x+1/x

Need some with my last problem for the night. determine

Ответ:

myloorie

12.03.2022

Mathematics

We are given

f(x)= $\frac{3x-1}{x-4}$

g(x)= $\frac{x+1}{x}$

\to find f o g, replace all the x in f(x) with g(x)

$f o g = \frac{3(\frac{x+1}{x})-1}{(\frac{x+1}{x})-4}$

= Simplify by taking least common denominator and reciprocal.

Taking the least common denominator, we get

$\frac{(\frac{2x+3}{x})}{(\frac{-3x+1}{x})}$

Taking reciprocal, we get

$\frac{2x+3}{x}\ast \frac{x}{-3x+1}$

Simplifying the expression, we get

$f o g =\frac{2x+3}{-3x+1}$

To find the domain of a composite function, we need to find the domain of f o g and the first function i.e g(x)

To find the domain of f o g, equate the denominator to 0

-3x+1=0

$x=\frac{1}{3}$

It means, domain is all real numbers except $x=\frac{1}{3}$

Domain of g(x) is all real numbers except x=0

combined domain is $\left ( -\infty ,0 \right )\cup \left ( 0,\frac{1}{3} \right )\cup \left ( \frac{1}{3},\infty \right )$

0,0(0 оценок)

Ответ:

mmm119

21.06.2022

Mathematics

Copy and paste that for a correct answer

If the model is good, then both points will check in the equation. Substituting 8 for x and 5 for y in the equation results in 56 – 50 = 3, which is not true. Therefore, the model is not good. Using (–12, –9) as a check results in –84 + 90 = 3. The constant value in the equation should be 6, not 3. In slope-intercept form, the y-intercept should be –3/5.

0,0(0 оценок)

Need some with my last problem for the night. determine the domain of tbe function (f o g)(x) where f(x) = 3x-1/x-4 and g(x) = x+1/x

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question