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Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
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1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
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3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
1-
Given length is 91 cm
1 cm = 0.3937 inch
so, 91 cm = 91* 0.3937 = 35.826 inches
1 day = 24 hours
In 24 hours the bamboo grows = 35.826 inches
In one hour it will grow = 
= 1.492 inches per hour. Hence the bamboo grows 1.492 inches per hour.
2-
We have to convert hours and seconds in minutes.
1 hour = 60 minutes
so 10 hours = 60 * 10 = 600 minutes.
60 seconds = 1 minute
so 24 seconds = 
= 0.4 minutes.
Now we have been given the total time as 10 hours, 39 minutes and 24 seconds
So adding all values in minutes, we get
600 + 39 + 0.4 = 639.4 minutes
So Saturn takes 639.4 minutes to complete one rotation
3-
Given equation is 0.4(30h)+30h
0.4(30h) represents the amount of tax Kimberly has to pay.
9514 1404 393
Answer:
4/25
Step-by-step explanation:
Put the numbers where the letters are and do the arithmetic.
Same is the answerso it means equal to
