Derivatives
derivative of x
1
Compostion of Functions
One function becomes the domain of the other
Domain
All of the input or x values in a function
1/x
x^-1
Inverse of f(x) = 2x+3
f^-1(x) = (x - 3)/2
derivative of 1/x
-1/(x^2)
How to prove algebraically that two functions are inverses
If f(g(x)) and g(f(x)) equal x, then f(x) and g(x) are inverses
Range
All of the actual output or y values in a function
√x
x^1/2
Find the inverse of the linear function y=1/2x+3
f(x)= 2x-6
derivative of a constant
0
If s(x) = x - 7 and t(x) = 4x^2 - x + 3, which expression is equivalent to (t*s)(x)?
4(x - 7)^2 - (x - 7) + 3
Vertical Line Test
A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation
(x^a)(x^b)
x^(a+b)
How to Find the Inverse of a One-To-One Function
1. Write y=f(x)
2. Solve the equation for x in terms of y
3. Interchange x and y; y= f^-1(x)
y= x^2+3x+8
d/dx= 2x+3
If h(x) = 5 + x and k(x) = 1/x, which expression is equivalent to (k*h)(x)?
1/(5 + x)
What is the domain of (7,6)(5,6)(7,2)(9,0)(4,3)
(4,5,7,9)
(x^a)^b
x^ab
Complete the statement that verifies that f(x) and g(x) are inverses: f(g(x))=g(f(x))=___
x
y= x^3+6x^2+5x+123
d/dx= 3x^2+12x+5
The function h(x) is given below.
h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)}
Which of the following gives h-1(x)?
B. {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
How can I find the domain of the function
f(t) = 1/(t+2)
you have a fraction, so you need to check first if there is a chance of having zero in the denominator.
2.- solve for t+2 = 0
t= -2
hence, t cannot take the value of -2 , for it would be impossible to divide over zero.
The domain is all the real numbers except -2
Zero Exponents Property
a⁰=1
Any number not equal to zero, raised to a power of 0 is 1.
If f(x) = x + 3 and g(x) = x - 3, are these inverse functions?
Yes