Composite Functions
What does this mean f(g(x))?
Put g(x) into f(x)
The domain of f is the what?
The range of f inverse
For exponents, what is the big number called?
The base
What is the base of a log in the calculator?
10
What is the word that Ms. Mosley uses to describe f(g(x))?
Fog
How do I find the domain of the composite functions?
Find the domain of what is being plugged in and find the domain of the simplified answer
What is the last step for finding the inverse of a function?
Verify that f(g(x)) = x and g(f(x)) =x
What is the domain of of exponential functions?
All real numbers
What is the domain of the natural log?
How do you write one-to-one with numbers
1:1
How do you show that two composite functions are equal?
f(g(x))=x and g(f(x)) =x
If the domain of a one-to-one function f is [0, inf), and its range is [5,inf). State the domain and range of f inverse.
Domain: [5, inf)
Range: [0,inf)
What is the inverse of the e^x?
The natural log
How do you write log base 5 of 10 is 21 as an exponent?
5^21=10
What test is used to show if a graph is 1:1?
Find the domain of f(g(x), it f(x)=3/(x-1) and g(x)=2/x
The domain is x can not be equal to 0, 2
Find the domain of the inverse of the f(x)= the square root of x
The domain is [0, positive infinity)
Solve this problem: (e^4)^x times e^(x^2) = e^12
x=-6, 2
Without using a calculator; log square root (10)
1/2 or .5
What did Ms. Mosley call the commandment of logs?
The rule log base a of x =y is a^y=x
Find the domain of g(f(x)), if f(x) = square root {x+2} and g(x)=x^2-4x+6
Domain: x is greater than or equal to 2
Find the inverse of the function:
f(x)=(x^2+3)/(3x^2) where x>0
f inverse = square root {(3)/(3x-1)}
If 4^x = 7, what does 4^-2x equal?
1/49
Solve the equation: log base 2 [(x-3)/(x+2)]
no solution
In class on Monday, we found the domain of this function log base 5 of [(x+1)/(x)], what topic or procedure we used?
Solving Rational Inequalities from Chapter 5 or using test points