Math 141 Final Exam Questions with100%
Correct Answers
One-to-One
Horizontal Line test, only one x for every y
Inverse Function
the function obtained by expressing the dependent variable of one function as the independent
variable of another f(g(x))=x and g(f(x))=x (if and only if F is one-to-one)
Inverse Symmetry
Symmetric with respect to line y=x
Derivative of Inverse
(f^-1)'(f(a))=1/(f'(a))
a^(x+y)
a^x * a^y
a^(x-y)
a^x/a^y
(a^x)^y
a^xy
(e^x)'
e^x * x'
, Domain and Range of e
Domain: R Range: (0,infinity)
Integral of e^kx
(1/k) * e^kx + C
Quadratic Formula
(-b +- root(b^2 - 4ac))/2a
y=log base a of x
a^y = x
a^(log base a of x)
x
log base a of a^x
x
e^lnx
x
lne^x
x
log(xy)
logx + logy
Correct Answers
One-to-One
Horizontal Line test, only one x for every y
Inverse Function
the function obtained by expressing the dependent variable of one function as the independent
variable of another f(g(x))=x and g(f(x))=x (if and only if F is one-to-one)
Inverse Symmetry
Symmetric with respect to line y=x
Derivative of Inverse
(f^-1)'(f(a))=1/(f'(a))
a^(x+y)
a^x * a^y
a^(x-y)
a^x/a^y
(a^x)^y
a^xy
(e^x)'
e^x * x'
, Domain and Range of e
Domain: R Range: (0,infinity)
Integral of e^kx
(1/k) * e^kx + C
Quadratic Formula
(-b +- root(b^2 - 4ac))/2a
y=log base a of x
a^y = x
a^(log base a of x)
x
log base a of a^x
x
e^lnx
x
lne^x
x
log(xy)
logx + logy
