Answers to the Inverse Relations and Functions Practice, cause I couldn't find it anywhere.
1. A relation is given in the table below. Write out the ordered pair for the inverse, and then determine is the inverse is a function.
B) (0,1), (1,2), (0,3), (2,4), (0,5); Inverse is not a function
2. A relation is shown in the graph below. Write out the ordered pairs for the inverse, and then determine if the inverse is a function.
B) (0,-1), (2,1), (-2,1), (3,3), (-3,3); inverse is a function
3. Find the inverse of the function, and then determine whether the inverse is a function. y = 3√x-5
C) y = x^3 + 5; inverse is a function
4. Find the inverse of the function, and then determine whether the invers is a function. y = x^2 + 4
A) y = ±√x-4; invers is not a function
5. Graph y = 3x^2 - 5 and its inverse
A) (You can check with mathway)
6. The formula for converting from Celsius to Fahrenheit temperatures if F = 9/5C + 32. Determine whether the original formula is a function, and whether the inverse is a function.
B) Original is a function; inverse is a function
7. Let f(x) = 10x - 10. Find he value of (f o f^-1)(-10)
D) -10
8. Without finding the invers of the function, determine the range of the inverse of f(x) = √x - 4
C) All real numbers greater that or equal to 4
9. Determine whether the statement below is always, sometimes, or never true.
The inverse of a cubic function is also a function
B) Sometimes true
10. Determine whether the statement below is always, sometimes, or never true.
A linear function has an inverse relation.
A) Always true
And the answers to the quick check:
1. B) Relation t is a function. The inverse of a relation t is a function.
2. A) y = ± √x+3/7
3. B) (Again, you can use mathway)
4. A) f^-1(x) = 7±√x/8; f^-1 is not a function
5. C) 4
Tea's answers are 100%
bless u
For 5 on the practice, the graph is A with one curvy line going up and another facing right
are these functions inverse functions
y=x-5
y=x+5
To find the answers to the Inverse Relations and Functions practice questions, we can follow the given steps for each question.
1. A relation is given in the table. To find the inverse, we swap the x and y values in each ordered pair. The inverse will be: (1, 0), (2, 1), (3, 0), (4, 2), (5, 0). To determine if the inverse is a function, we look for any repeated x-values. In this case, the x-value of 0 appears multiple times, so the inverse is not a function.
2. A relation is shown in the graph. To find the inverse, we reflect each point across the line y = x. The inverse will be: (−1, 0), (1, 2), (1, −2), (3, 3), (3, −3). To determine if the inverse is a function, we look for any repeated x-values. In this case, there are no repeated x-values, so the inverse is a function.
3. The original function is y = 3√(x−5). To find the inverse, we swap the x and y variables and solve for y. The inverse will be y = x^3 + 5. To determine if the inverse is a function, we look for any repeated x-values. In this case, there are no repeated x-values, so the inverse is a function.
4. The original function is y = x^2 + 4. To find the inverse, we swap the x and y variables and solve for y. The inverse will be y = ±√(x−4). To determine if the inverse is a function, we look for any repeated x-values. In this case, the x-value of 4 has two possible y-values, so the inverse is not a function.
5. To graph y = 3x^2 - 5 and its inverse, we can plot several points for each equation and connect them with a smooth curve. Alternatively, you can use graphing tools like Mathway to graph both equations.
6. The formula for converting Celsius to Fahrenheit temperatures is given as F = (9/5)C + 32. To determine if the original formula is a function, we check if each input value (Celsius temperature) has a unique output value (Fahrenheit temperature). In this case, each Celsius temperature corresponds to a unique Fahrenheit temperature, so the original formula is a function. To determine if the inverse is a function, we repeat the same check, but with Fahrenheit temperatures as input and Celsius temperatures as output. In this case, each Fahrenheit temperature also corresponds to a unique Celsius temperature, so the inverse is a function.
7. Let f(x) = 10x - 10. To find (f o f^−1)(−10), we need to find f^−1(x) and then substitute −10 for x in f^−1(x). To find f^−1(x), we swap the variables and solve for x. f^−1(x) = (x + 10)/10. Substituting −10 into f^−1(x), we get (-10 + 10)/10 = 0. Therefore, (f o f^−1)(−10) = 0.
8. Without finding the inverse, we can determine the range of the inverse of f(x) = √(x-4). The range of the inverse will be all the possible values that x can take. In this case, x is under the square root, so it must be greater than or equal to 4 to avoid taking the square root of a negative number. Therefore, the range of the inverse is all real numbers greater than or equal to 4.
9. The statement "The inverse of a cubic function is also a function" is sometimes true. It depends on the specific cubic function. Some cubic functions may have inverses that are functions, while others may not. To determine if a specific cubic function has an inverse function, we need to check if each x-value has a unique y-value and vice versa.
10. The statement "A linear function has an inverse relation" is always true. In general, linear functions have inverses that are relations. For every x-value, there will be a unique y-value, and vice versa. However, not all linear functions have inverses that are functions. It depends on whether there are repeated x-values in the original function.