Let f(x) = x^2 + x, and g(x) = x^2 - 1. Find each function and its domain: a. (f + g)(x)\b.(\frac{f}{g})(x) Let f(x) = ln (sec(x) ) on the domain -pi/2 < x < pi/2. So find f'(x). Find the domain algebraically without a graph of f(x) ...
I get the x-stuff by itself on one side of the "equals" sign: xy = 5y − 2 Then I solve for x=: And then switch the x's and y's: So I've found the inverse, and it's another rational function; in particular, the inverse is indeed a function. The domain and range of ...
Find the domain and range of the function defined below: f(x) = \begin{cases} x+2 & \text{ for } x 4, \\ \frac{3}{4} x + 4 & \text{ for } x \geq 4. \end{cases} Find the domain and range of the function y = f(...
The domain of a function is the set of all real numbers that can be used as an input to give a real number as the output. The range of a function is the set of all outputs. Answer and Explanation:1 Note thaty=secx=1cosx ...
Algebraically, this can be represented by saying a function has a period p iff f(x)=f(x+p) for all x values in its domain. If a periodic function is continuous, then it must have a maximum and minimum value. The amplitude of a periodic function is half of the difference between its...
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Find the domain of g(y), and this will be the range of f(x). ... If you can't seem to solve for x, then try graphing the function to find the range. Is a ray two dimensional? Ray: A 2-dimensional figure that has one endpoint and goes without end in one direction. A ray...
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1. Find (fºg)(x), (gºf)(x), and determine the domain for each of the composite functions. a) f(x) = 4 - 2x' and g(x) = 3x - 5. b) f(x)=6x – 3 and g(x)= 77-2x. 2. A blouse that is size x in Jap...
EXAMPLE 4 Find the inverse of a power function The domain of f is restricted to nonnegative values of x. So, the range of f –1 must also be restricted to nonnegative values, and therefore the inverse is f –1(x) = x. (If the domain was restricted to x ≤ 0, you would choose...