Inverse Functions
Find the inverse function of
f(x)=(x+1)/6
f-1(x)=6x-1
Find the equation of the line with a slope of 1/2 and y-intercept (0, 3)
y=1/2x+3
Find a mathematical model that represents Boyle's law which says: for a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas.
P=k/V
What is the end behavior of the function:
f(x)=-3x6+5x5-6x4-2x2+1
as x-> infinity, y-> - infinity
as x-> - infinity, y -> infinity
State the domain the function:
f(x)=(x-4)/(x-7)
(-inf, 7) U (7, inf)
f(x)=sqrt(2x+3)
f-1(x)=(x2-3)/2, x>=0
Find the equation of the line parallel to y=-2x+4 and y-intercept (0, 5)
y=-2x+5
Find the mathematical model that represents the statement: z varies directly as the square of x and inversely as y.
z=6 when x=6 and y=4.
z=2x2/3y
Fully factor the function:
f(x)=x4-4x3-7x2+22x+24, given that -2 and 3 are zeros.
f(x)=(x+2)(x-3)(x+1)(x-4)
Solve:
2/(x+1)>= 3/(x-1)
[-5, -1)U(1, inf)
f(x)=(x+3)2
restrict the domain x>=3
f-1(x)=sqrt(x)-3
Find the equation of the line that goes through (5, -2) and (-1, 4)
y=-x+3
The power P produced by a wind turbine varies directly as the cube of the wind speed S. A wind speed pf 27 mph produces a power output pf 750 KW. Find the output for a wind speed of 40mph.
2438.64kW
Find the zeros of the function, given that 2+i is a zero.
f(x)=2x4-3x3-13x2+37x-15
-3, 1/2, 2+i, 2-i
Find all intercepts of
f(x)=(6x2-7x+2)/(4x2-1)
y-int: (0, -1/2)
x-int: (2/3, 0) and (1/2, 0)
f(x)=(5x-3)/(2x+5)
f-1(x)=(5x+3)/(5-2x)
Find the equation of the line perpendicular to 5x-4y=8 and goes through the point (3, -2)
y=-4/5x+2/5
The fundamental frequency (in Hertz) of a piano string is directly proportional to the square root of its tension and inversely proportional to the square root of its tension and inversely proportional to its length and the square root of its mass density. A string has a frequency of 100 hertz. Find the frequency with twice the length.
50 Hz
Find the zeros of the function:
f(x) = 3x3+14x2-7x-10
x=-5, -2/3, 1
Find the all asymptotes of
f(x)=8/(x2-10x+24)
VA: x=4, x=6
HA: y=0
f(x)=2(x-4)2+3
restrict domain x>=4
f-1(x)=sqrt((x-3)/2) +4
A manuscript charges a starting fee of $50 plus $2.50 per page translated. Write a linear equation for the amount A earned for translating p pages.
A=2.50p+50
The maximum load that a horizontal beam can safely support varies jointly as the width of the beam and the square of its depth and inversely as the length of the beam. Determine how halving the width and doubling the length affects the beam's maximum load.
The safe load is 1/4th as great.
Find all zeros of the function:
f(x) = x4-9x2-22x-24
x=-2, 4, sqrt(2)i, -sqrt(2)i
Find all asymptotes of
f(x)=(2x2+2)/(x+1)
VA: x=-1
SA: y=2x-2