For the functionn f(x) = 5 √x/5
find f^-1(x)
The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th.
score. Number of students
80. 5
85 9
90 5
95 6
100 9
I think it's pretty clear that it should have been f(x) = 5√(x/5)
To find the inverse of a function, we usually switch the roles of x and y and then solve for y.
Step 1: Replace f(x) with y.
y = 5 √(x/5)
Step 2: Swap x and y.
x = 5 √(y/5)
Step 3: Isolate y.
x = 5 √(y/5)
Divide both sides by 5.
x/5 = √(y/5)
Step 4: Remove the square root by squaring both sides.
(x/5)² = (y/5)
Step 5: Multiply both sides by 5.
5(x/5)² = 5(y/5)
x²/25 = y/5
Step 6: Multiply both sides by 5.
5(x²/25) = 5(y/5)
x²/5 = y
Step 7: Replace y with f^-1(x).
f^-1(x) = x²/5
Therefore, the inverse of the function f(x) = 5 √(x/5) is f^-1(x) = x²/5.
To find the inverse of a function, f^-1(x), you need to follow a few steps:
Step 1: Replace f(x) with y.
y = 5√(x/5)
Step 2: Swap x and y to obtain the equation in terms of x.
x = 5√(y/5)
Step 3: Solve the equation for y.
To solve for y, we need to isolate it on one side of the equation.
Begin by dividing both sides of the equation by 5, and then square both sides to eliminate the square root.
(x/5) = (√(y/5))^2
(x/5) = (y/5)
y = x/5
Step 4: Replace y with f^-1(x) to get the inverse function.
f^-1(x) = x/5
Therefore, the inverse of f(x) = 5√(x/5) is f^-1(x) = x/5.
We can start by setting y = f(x) and solving for x:
y = f(x) = 5 √x/5 = √x
Squaring both sides, we get:
y^2 = x
Now, we can switch x and y to get the inverse function:
f^-1(x) = y = √x
Therefore, the inverse function of f(x) = 5 √x/5 is f^-1(x) = √x.
You are correct. The correct function is f(x) = 5 √(x/5). Thank you for bringing that to our attention.
To find the mean of the scores in the table, we need to first calculate the sum of all the scores, which is:
(80 × 5) + (85 × 9) + (90 × 5) + (95 × 6) + (100 × 9) = 2355
Next, we need to calculate the total number of students, which is:
5 + 9 + 5 + 6 + 9 = 34
Finally, we can find the mean by dividing the sum by the total number of students:
2355 / 34 = 69.26 (rounded to the nearest tenth)
Therefore, the mean score is 69.3.