calculus please
posted by jane .
given f(x) = abs(sin x) and g(x) = x^2 for all real x:
1) let H(x) = g(f(x)) and write an expression for it.
2) find domain and range of H(x).
3) find an equation of the line tangent to the graph of H at the point where x = pi/4.

Since g(x) involves squaring x, you don't need the "absolute value" symbol when considering g(f(x)). You get the same result if you square a negative sinx. Thus
H(x) = g(f(x)) = sin^2 x
The domain is all real x and the range is from 0 to 1
At x = pi/4, H(x) = [sqrt2/2]^2 = 1/2
The slope dH/dx there is 2 sin x cos x = 1
So, find the equation of a line through x = pi/4, H = y = 1/2 with slope = 1
(y  1/2)/(x  pi/4)= 1
y  1/2 = x  pi/4
y = x + 1/2  pi/4)
I am calling H(x) "y" in the graph of the function 
i forgot the part that said "for pi is less than or equal to x is less less than or equal to pi"
this was attached to the f(x)  does it change the answer? the domain?
Respond to this Question
Similar Questions

algebra
Find the domain and range of the function. 1. f(x)= x^2x I got: Domain= All Real Numbers Range= All Real Numbers > 1 (with a line under the greater than sign) 2. f(x)= 1x^2 I got: Domain= All Real Numbers Range= All Real Numbers … 
Precalculus
Can somebody help me wit this? Find the range and the domain of: f(x)=(1/2)x2 The domain is all real numbers (x) from infinity to infinity The range (of f(x)) is 0 to infinity, since it can never be negative. f(x) has a minimum 
Calculus
I'm doing graphs/domain/range of basic functions. I have three questions: How do I find the domain and range of a function? 
Math
If f(x)=sin(x) and g(x)=x^2x+1, find the domain of f(g(x)) and g(f(x)). I was able to determine that: f(g(x))= sin(x^2x+1) and g(f(x))= sin(x)^2 sin(x) +1 Here is what I am thinking: the range of f(x) is (x e R) and the range of … 
calculus
given the following piecewise function x+11 for 9<=x<3 y= { 2 for 3<=x<=2 2x6 for 2<x<=5 a. find the domain b. find the range c. find the intercepts d. is f continuos on its domain. If not, state where f is discontinious … 
algebra
Can someone check my answers please and if Im wrong please explain. 1) graph 4x^2+4y^2=64. what are the domain and range? 
algebra
Find the domain and range of the relation and determine whether it is a function? 
algebra
can someone help me find the domain and range of the function f(x)=3(x3)^21 I think the domain is all real numbers but I'm not sure about the range 
Math
Find the domain and range for y=x^2+9. Wouldn't the domain and range just be all real numbers since nothing else is really given in the equation? 
Math
What is the domain and range fro the expentiral function f(x)=2x4^x1+3?