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3 years ago

(fog)(x) and (gof)(x) f(x)= 8/1-5x g(x)= 1/x Then find the domain for each

Mathematics

1 answer:

Paha777 [63]3 years ago

5 0

To find FoG ( or F of G) you put the equation of G in for the X of F

FoG = $\frac{8x}{x-5}$ The domain is All Except 5 since it makes the bottom 0

GoF = $- \frac{5x}{8} + \frac{1}{8}$ The domain is -Infinity to Infinity

FoG --- The picture --- You want the denominator the same for both of the numbers. By turning 1 into 1x/x it still stays 1 because the x's cancel out, but it can group with the 5.

Next you can multiply both sides (top and bottom) by x and get the final product.

GoF --- Multiply both sides by 5x+1 and get the final product

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If h(x)=(fog)(x) and h(x)=³√x+3, find g(x) if f(x) =³√x+2

ipn [44]

Answer:

$g(x)=x+1$

The problem:

Find $g(x)$ if $h(x)=(f \circ g)(x)$ ,

$h(x)=\sqrt[3]{x+3}$ , and

$f(x)=\sqrt[3]{x+2}$ .

Step-by-step explanation:

$h(x)=(f \circ g)(x)$

$h(x)=f(g(x))$

Replace $x$ in $f(x)=\sqrt[3]{x+2}$ with $g(x)$ since we are asked to find $f(g(x))$ :

$\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}$

$\sqrt[3]{x+1+2}=\sqrt[3]{g(x)+2}$

This implies that $x+1=g(x)$

Let's check:

$(f \circ g)(x)$

$f(g(x))$

$f(x+1)$

$\sqrt[3]{(x+1)+2}$

$\sqrt[3]{x+1+2}$

$\sqrt[3]{x+3}$ which is the required result for $h(x)$ .

6 0

3 years ago

Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of e

emmainna [20.7K]

This question is incomplete, the complete question is;

Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) The line passes through the point (3, 1, 2) and is parallel to the line given by x = y = z.

Answer:

the set of parametric equations of the line with the given characteristics are; x = t+3, y = t+1, z = t+2

Step-by-step explanation:

Given that;

line x = y = z and point ( 3, 1, 2 )

the given line can be written as;

[x-0 / 1] = [y-0 / 1] = [z-0 / 1]

if two lines are parallel directional ratios are equal.

so DIRECTIONAL RATIOS of given line is ( 1, 1, 1 )

therefore required line is;

[x-3 / 1] = [y-1 / 1] = [z-2 / 1] = t

⇒ [x-3 / 1] = t

x = t+3

[y-1 / 1] = t

y = t+1

[z-2 / 1] = t

z = t+2

Therefore the set of parametric equations of the line with the given characteristics are; x = t+3, y = t+1, z = t+2

8 0

3 years ago

Kyle is having a party he has 43 hot dogs there will be 8 people at his party how many hotdogs will each person get

Brrunno [24]

each person will get 5 hot dogs.

Step-by-step explanation:

Total number of Hot dogs =43

Total number of people at party= 8

Each person will get hot dogs= $\frac{Total number of Hot dogs}{Total number of people at party }$

Each person will get hot dogs= $\frac{43}{8}$

Each person will get hot dogs= 5.37 or ≈ 5

So, each person will get 5 hot dogs.

Keywords: Word Problems

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6 0

3 years ago

How would you find the volume of the solid in the figure shown above?

Natasha_Volkova [10]

The answer is D and it's pretty simple to do:

$V_{1}=a*b*c\\
V_{2}= \pi r^{2} h\\
V_{3}= \frac{1}{3} \pi r^{2}h$

5 0

3 years ago

Read 2 more answers

What's the difference?<br> -1 1/8 - 6/8=

sergejj [24]

Answer: -3/8

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers