Step OneFor convenience f(x) = y
y = -(1/2) sqrt(x + 3) Interchange x and y
x = -(1/2) sqrt(y + 3) Multiply both sides by -2
(-2x) = sqrt(y + 3) Square both sides
4x^2 = y + 3 Subtract 3 from both sides
4x^2 -3 = y
f-1(x) = 4x^2 - 3
GraphsThe original graph is in blue
The inverse is red.
Green Line y = x : explained below.
CommentInverses have a very strange property. It acts as a check.
If you perform the following operation
f-1(f(x)) you are left with x
In this case f-1[-1/2 sqrt(x + 3)]= 4(-1/2 * sqrt(x + 3))^2 - 3
f-1 (-1/2sqrt(x+3)) = 4 (1/4 (x+3) - 3
f-1(-1/2sqrt(x + 3)) = x+ 3 - 3 = x
I've included this because I think you have to put the same restriction on f-1(x) as you do on f(x) which is that for f(x) x ≥ -3
This last assertion could be incorrect, but I don't think so.
The answer is f-1(x) = 4x^2 - 3 <<<<<
answer first box and
x≥-3 for the second box. <<<<<<
answer for the second box.Let me know if these are correct. I'm not sure about the restrictions.
The unit rate is $7.75 because 46.50 divide by 6 is $7.75
You could maybe think about the numbers like fractions,decimals and never ending numbers.
Answer:
x = 1 or x = -5 or x = 10
Step-by-step explanation:
f(x) = x³ – 6x² – 45x + 50 = (x² + 4x -5) (x - 10) = (x - 1) (x + 5) (x - 10)
(x - 1) (x + 5) (x - 10) = 0
x = 1 or x = -5 or x = 10
Answer:
The average rate of movement along the San Andreas Fault is between 30mm and 50mm per year over the last 10 million years. If current rates of movement are maintained Los Angeles will be adjacent to San Francisco in approximately 20 million years.
Step-by-step explanation: