quadratic functions
This is the vertex for the parabola represented by the quadratic function:
f(x) = (x-2)^2 + 3
this is the logarithm log_5 125 = 3 in exponential form
what is 5^3 = 125
is the function
f(x) = x^3 - 4x one to one?
Using the laws of logs, this is the following expression combined in a single log.
3log(5) + log(4) - log(2)
log(250)
f(x) = 2x^2 - 8x + 5
(h,k) = (2,3)
This is the exponential equality 4^3 = 64 in logarithmic form
log_4 64 = 3
This is the inverse of this function:
f(x) = (2x+5)/(x-3)
f^-1(x) = (3x+5)/(x-2)
4^(x+3) = 1
x = -3
this is the standard form for f(x) = 3x^2 - 12x + 7
f(x) = 3(x-2)^2 - 5
this is the value of x for log_5(x) = 4
x = 5^4 = 625
f(x) = 3x+2
g(x) = (x-2)/3
checking f(g(x)) = x and g(f(x)) = x so yes
solve the equation 6*10^(2x-1) = 48
x = 1/2 + log(8)/2 or x = 1/2 + ln(8)/2ln(10)
This is the price that will yield a maximum weekly revenue The landscaping company earns weekly revenue R based on the price they charge per lawn service hour, p, given by equation:
R(p) = -15p^2 + 450p
the best price is when p = $15
this is x where ln(e^x) = 123
x = 123
find the inverse of the problem
f(x) = 3/(x+2) and give its domain and range of both f(x) and f^-1(x)
f^-1(x) = (3-2x)/x
ln(x+4) + ln(3) = ln(21)
x =3