3x+1
1. A function f: x →
X-1
(i)
Find the images of -1 and 3.
(ii)
Find the value of x for which f(x) = 7
2. The set P = {-2,-1,0,1,2} maps onto Q by the function f(x)=x²-2, where x E P.
(i)
Find the elements of Q.
(ii)
3. Given that f(x) = 2x - 1 and g(x) = x² +1:
Find f(1 + x):
Find the range of values of x for which f(x) < -3;
Simplify f(x) - g(x).
(i)
(ii)
(iii)
,x # 1, is defined on the set (-1, 0, 2, 3, 4, 5)
Draw a diagram showing the mapping between P and Q.
(i)
4. The function f and g are defined as follows: f:x →→ 2
x-1 and g:x→ 3x + 1
Evaluate f(-) +1
(ii)
Solve f(x) = g(-2)
5. Given that f(x) = px + q, find the values od p and q, if f(2)= 4 and f(4) == 10
The function f is defined as f:x→ 3x² - 5x.
6.
(i)
Evaluate f(--3)
(ii)
7. The functions f and g are defined as: f:xx-2 and g: x2x²-1. Solve:
(i) f(x) = g(-²/-) (ii) f(x) + g(x)= 0
4
Find the values of x for which f(x) = -² 3

On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]

x = 0 , y = -1 so c = -1.

slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]

function f(x) = -5x - 1.

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Answer:

Step-by-step explanation:

1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10

(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:

3x + 1 = 7

3x = 6

x = 2

2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}

(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}

3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1

(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:

2x - 1 < -3

2x < -2

x < -1

so x can be any value less than -1

(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2

4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1

(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:

2x - 1 = 3(-2) + 1

2x - 1 = -5

2x = -6

x = -3

5. f(x) = px + q, given that f(2)= 4 and f(4) == 10

so

4 = 2p + q

10 = 4p + q

solving for p and q we get p = 3 and q = -2

6. (i) f(--3) = 3(-3)² - 5(-3) = -27

7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:

x-2 = (1/4)x² - 1

x-2 = x²/4 - 1

4x-8 = x²-4

x²-4x+4 = 0

x = 2, -2

(ii) To solve f(x) + g(x) = 0

x-2 + x²-1 = 0

x²-2x+1 = 0

(x-1)² = 0

x = 1

for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3

into the expression of f(x) = 3x² - 5x

3x² - 5x = -3

3x² - 5

What is the volume of one cylinder ??

A 1948 study in Biometrika investigated the effects of several different diets on the weight of chickens. In this study, chickens were randomly assigned to one of several different groups, and each group of chickens received a different type of feed. The data provided represent a subset of data from this study and show the weights (in grams) of chickens receiving the sunflower, meatmeal, soybean, and casein feeds.
Use software to conduct an analysis of variance (ANOVA) ????F‑test to test the claim that the mean weights of chickens receiving sunflower, meatmeal, soybean, and casein are equal. What are the ????F‑statistic and pp‑value for this test? Please round your ????F‑statistic to the nearest two decimal places and your pp‑value to the nearest five decimal places.
1. ????F‑statistic :
2. pp‑value :
Based on the pp‑value for this ANOVA ????F‑test, select the correct conclusion at the ????=0.05α=0.05 level.
a. Since the pp‑value is greater than ????=0.05α=0.05, there is little evidence of a difference in the mean weights of chickens receiving the sunflower, meatmeal, soybean, and casein feeds.
b. Since the pp‑value is less than ????=0.05α=0.05, there is significant evidence of a difference in the mean weights of chickens receiving the sunflower, meatmeal, soybean, and casein feeds.
c. Since the pp‑value is less than ????=0.05α=0.05, there is little evidence of a difference in the mean weights of chickens receiving the sunflower, meatmeal, soybean, and casein feeds.
d. Since the pp‑value is greater than ????=0.05α=0.05, there is significant evidence of a difference in the mean weights of chickens receiving the sunflower, meatmeal, soybean, and casein feeds.
weight feed
368 1
390 1
379 1
260 1
404 1
318 1
352 1
359 1
216 1
222 1
283 1
332 1
325 2
257 2
303 2
315 2
380 2
153 2
263 2
242 2
206 2
344 2
258 2
243 3
230 3
248 3
327 3
329 3
250 3
193 3
271 3
316 3
267 3
199 3
171 3
158 3
248 3
423 4
340 4
392 4
339 4
341 4
226 4
320 4
295 4
334 4
322 4
297 4
318 4

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