Posted by Julie on Sunday, February 10, 2013 at 10:35pm.
The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the input for a second function g(x). In this case, the composite is denoted g(f(x)) which is read "g composed with f of x" or "g of f of x."
**If you could help with anything I'd really appreciate it!! Thank you**
Suppose f and g are functions defined by the following table:
x) -3 -2 -1 0 1 2 3
f(x) 10 8 7 3 -4 -7 -8
g(x) 3 1 0 2 -3 -1 -2
i. Make a table of values for f(g(x)) with x= -3,-2,-1,0,1,2,3 Remember to always start with the innermost set of parentheses
ii. Make a table of values for g(g(x)) with x= -3,-2,-1,0,1,2,3.
iii. Explain why you cannot find the composite function g(f(x)).
a)Consider the two functions f(x)=-x^2+ 7 and g(x)=3x+4. Using input values of -1,2,0.5,and 8 for x:
1. Calculate f(g(x)) for each input value
2. Calculate g(f(x)) for each input value.
B) if f and g are two functions, what must be true about the domains and ranges of f and g in order for f(g(x)) to make sense? What must be true for g(f(x))to make sense?
- Precalculus - Katy, Thursday, February 12, 2015 at 8:22pm
If (f º g)(3) = 7, then f(x) and g(x) could be:
a. f(x) = 3x2 – 10x + 4, g(x) = x + 2
b. f(x) = 2x – 3, g(x) = x2 – 4
c. f(x) = 3x + 1, g(x) = x – 3
d. f(x) = x2, g(x) = x – 2
Answer This Question
More Related Questions
- math - The application of one function followed by the application of a second ...
- advanced functions/precalculus - 1. The function f(x) = (2x + 3)^7 is the ...
- Math - Redo problem 13 from section 1.8 of your textbook (page 62), but use the ...
- math - (a) In order to express the function y = 1010 x + 4, as a composition of ...
- Calculus - In order to express the function y=12^19x+7 as a composition of two ...
- Algebra Functions - I cannot for the life of me remember how to do this- Find ...
- college algebra - find a real-life application of a quadratic function. State ...
- Math, Still Need Help! - Label each statement TRUE or FALSE. a. The sum of two ...
- Math - a) In order to express the function y = 1311 x − 4, as a ...
- Need Help!! Algebra - I am having trouble in this class and need help with this ...