Posted by **jane** on Thursday, February 19, 2009 at 11:15pm.

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.

- calculus please -
**drwls**, Thursday, February 19, 2009 at 11:58pm
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

- calculus please -
**jane**, Friday, February 20, 2009 at 12:08am
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?

## Answer This Question

## Related Questions

- Calculus - I'm doing graphs/domain/range of basic functions. I have three ...
- algebra - Can someone check my answers please and if Im wrong please explain. 1...
- Math - If f(x)=sin(x) and g(x)=x^2-x+1, find the domain of f(g(x)) and g(f(x)). ...
- algebra - Find the domain and range of the function. 1. f(x)= x^2-x I got: ...
- Math - Find the domain and range for y=x^2+9. Wouldn't the domain and range just...
- calculus - given the following piecewise function x+11 for -9<=x<-3 y= { 2...
- algebra - Find the domain and range of the relation and determine whether it is ...
- Pre-calculus - Can somebody help me wit this? Find the range and the domain of: ...
- algebra - can someone help me find the domain and range of the function f(x)=3(x...
- Calculus - Find the sum and difference functions f + g and f – g for the ...

More Related Questions