recall that for inverse functions, <u>the range of the original is the domain of the inverse</u> and othe other way around.
so f⁻¹(8) is f⁻¹(x) but making x = 8, so the domain value in this case for the inverse is 8, and that's going to give us something, but let's nevermind that.
since the domain value is 8 for the inverse, that means, the same 8, is a range for the original f(x).
meaning, "some value of x" on the original, gives us a range of 8, then let's use that 8 in the original, BUT not on "x", but on "y", or f(x).
![\bf f^{-1}(8)~\hspace{7em}\stackrel{f(x)}{8}=2x+5 \\\\[-0.35em] ~\dotfill\\\\ 8=2x+5\implies 3=2x\implies \boxed{\cfrac{3}{2}=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{original f(x)}}{\left(\stackrel{x}{\frac{3}{2}}~~,~~\stackrel{y}{8} \right)}~\hspace{7em} \stackrel{\textit{inverse }f^{-1}(x)}{\left(\stackrel{x}{8}~~,~~\stackrel{y}{\frac{3}{2}} \right)}~\hfill f^{-1}(8)=\cfrac{3}{2}](https://tex.z-dn.net/?f=%5Cbf%20f%5E%7B-1%7D%288%29~%5Chspace%7B7em%7D%5Cstackrel%7Bf%28x%29%7D%7B8%7D%3D2x%2B5%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%208%3D2x%2B5%5Cimplies%203%3D2x%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B3%7D%7B2%7D%3Dx%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Boriginal%20f%28x%29%7D%7D%7B%5Cleft%28%5Cstackrel%7Bx%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D~~%2C~~%5Cstackrel%7By%7D%7B8%7D%20%5Cright%29%7D~%5Chspace%7B7em%7D%20%5Cstackrel%7B%5Ctextit%7Binverse%20%7Df%5E%7B-1%7D%28x%29%7D%7B%5Cleft%28%5Cstackrel%7Bx%7D%7B8%7D~~%2C~~%5Cstackrel%7By%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5Cright%29%7D~%5Chfill%20f%5E%7B-1%7D%288%29%3D%5Ccfrac%7B3%7D%7B2%7D)
so notice how the values swap places for the inverses, one's domain, is the other's range.
Answer:
The test statistic Z = 3.125
Step-by-step explanation:
<em>Given Population proportion P = 0.25</em>
<em>Given sample size 'n' = 696</em>
<em>Sample proportion 'p⁻' = 0.30</em>
Test statistic
<u><em>Final answer</em></u>:-
The test statistic Z = 3.125
Answer:
v = - 3
Step-by-step explanation:
Given
v = u + at ← substitute u = 2, a = - 5, t = 1 into the expression
v = 2 + (- 5 × 1) = 2 + (- 5) = 2 - 5 = - 3
Using arithmetic and the information provided, there were 6 persons at the party.
<h3>Number of people at the party</h3>
The question is asking us to use the cost of the plates served to each person to calculate the number of people in the party from the information available in the question.
- Normal charge of a plate of food = $95
- Additional charge on each plate of food = $12.75
- Total cost of the party = $656
- Total cost of food for each person = $95 + $12.75 = $107.75
Number of people at the party can be obtained from; Total cost of food at the party/ Total cost of each plate of food
= $656/ $107.75 = 6 persons
Learn more about arithmetic: brainly.com/question/2171130
Answer:
$650
Step-by-step explanation:
$50 + $75(8)
= $50+ $600
= $650
