Answer:
yesyesyesyes
Step-by-step explanation:
yesyesyesyesyes
f(x)=x3−5
Replace f(x)
with y
.
y=x3−5
Interchange the variables.
x=y3−5
Solve for y
.
Since y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
y3−5=x
Add 5
to both sides of the equation.
y3=5+x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=3√5+x
Solve for y
and replace with f−1(x)
.
Replace the y
with f−1(x)
to show the final answer.
f−1(x)=3√5+x
Set up the composite result function.
f(g(x))
Evaluate f(g(x))
by substituting in the value of g into f
.
(3√5+x)3−5
Simplify each term.
Remove parentheses around 3√5+x
.
f(3√5+x)=3√5+x3−5
Rewrite 3√5+x3
as 5+x
.
f(3√5+x)=5+x−5
Simplify by subtracting numbers.
.
Subtract 5
from 5
.
f(3√5+x)=x+0
Add x
and 0
.
f(3√5+x)=x
Since f(g(x))=x
, f−1(x)=3√5+x is the inverse of f(x)=x3−5
.
f−1(x)=3√5+x
Answer:

Step-by-step explanation:
![\sf{ [ (4 \frac{1}{6} + 2 \frac{1}{3} ) \div 4 \frac{1}{3}] - 1\frac{1}{2} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5B%20%284%20%5Cfrac%7B1%7D%7B6%7D%20%20%2B%202%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%20%5Cdiv%204%20%5Cfrac%7B1%7D%7B3%7D%5D%20-%20%201%5Cfrac%7B1%7D%7B2%7D%20%7D)
Convert the mixed numbers into improper fraction
![\longrightarrow{ \sf{ [ ( \frac{25}{6} + \frac{7}{3} ) \div \frac{13}{3}] - \frac{3}{2}}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%20%28%20%5Cfrac%7B25%7D%7B6%7D%20%20%2B%20%20%5Cfrac%7B7%7D%7B3%7D%20%29%20%5Cdiv%20%20%5Cfrac%7B13%7D%7B3%7D%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%7D%7D%20)
Add the fractions : 25 / 6 and 7 / 3
While performing addition or subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fraction.
To do so, first take the L.C.M of 6 and 3 which results to 6
![\longrightarrow\sf{ [( \frac{25 + 7 \times 2}{6} ) \div \frac{13}{3} ] - \frac{3}{2}}](https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%5Csf%7B%20%5B%28%20%5Cfrac%7B25%20%2B%207%20%5Ctimes%202%7D%7B6%7D%20%29%20%5Cdiv%20%20%5Cfrac%7B13%7D%7B3%7D%20%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%7D%20)
![\longrightarrow{ \sf{ [( \frac{25 + 14}{6} ) \div \frac{13}{3} ] - \frac{3}{2} }}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%28%20%5Cfrac%7B25%20%2B%2014%7D%7B6%7D%20%29%20%20%5Cdiv%20%20%5Cfrac%7B13%7D%7B3%7D%20%20%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%7D%7D)
![\longrightarrow{ \sf{ [ \frac{39}{6} \div \frac{13}{3}] - \frac{3}{2} }}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%20%5Cfrac%7B39%7D%7B6%7D%20%20%5Cdiv%20%20%5Cfrac%7B13%7D%7B3%7D%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%7D%7D)
Multiply the dividend by the reciprocal of the divisor.
Reciprocal of any number or fraction can be obtained by interchanging the position of numerator and denominator
![\longrightarrow{ \sf{ [ \frac{39}{6} \times \frac{3}{13} ] - \frac{3}{2}}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%20%20%5Cfrac%7B39%7D%7B6%7D%20%20%5Ctimes%20%20%5Cfrac%7B3%7D%7B13%7D%20%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%7D%7D%20)
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term
![\longrightarrow{ \sf{ [ \frac{39 \times 3}{6 \times 13} ] - \frac{3}{2}}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%20%20%5Cfrac%7B39%20%5Ctimes%203%7D%7B6%20%5Ctimes%2013%7D%20%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%7D%7D%20)
![\longrightarrow{ \sf{ [ \frac{117}{78} ] - \frac{3}{2} }}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20%5B%20%20%5Cfrac%7B117%7D%7B78%7D%20%20%5D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%7D%7D)

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same

Subtract 3 from 3

Divide 0 by 2

Hope I helped!
Best regards!
Answer:
The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.
Step-by-step explanation:
Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs (
) after a certain amount of years (t) is given by the following formula:

Where:
- Initial amount of jobs in pipe fitting industry, measured in thousands.
- Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)
If
,
and
, then:


The percent change in jobs from pipe fitting industry is calculated as follows:



The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.
Let the width = w.
The length is 6 times the width, so the length is 6w.
The perimeter is 70.
P = 2L + 2W
70 = 2(6w) + 2(w)
70 = 12w + 4w
70 = 14w
5 = w
The width is 5.
The length is 6 times the width, so the length is 6 * 5 = 30
Area of rectangle = LW
A = 5 * 30 = 150