9514 1404 393
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:
$768
Step-by-step explanation:
A = lw
A = 16(8)
A = 128
128*6 = 768
For every c substitute 4 and for every d substitute -2
c=4
d=-2
6c + 5d - 4c - 3d + 3c - 6d
= 6(4)+ 5(-2)- 4(4)- 3(-2)+ 3(4)- 6(-2)
=24+(-10)-16-(-6)+12-(-12)
=24-10-16+6+12+12
=28
Answer:
2 : 3
Step-by-step explanation:
You need to show the ratio using the smallest whole numbers possible.
Multiply both numbers by 3.
2/3 : 1
2/3 × 3 : 1 × 3
2 : 3
