functions problem

• Dec 5th 2008, 12:41 PM
kim1709
functions problem
I have a few problems I would be VERY thankful to have some help with. Thank you in advance!

1. Determine whether the pair is parallel, perpendicular, or neither.
6x+2y=8
18x+6y=25

2. Find the given value.
Find (f*g)(2) when f(x)=x+1 and g(x)= -3x^2 +15x-5

3. Find the domain of the composite function f*g
f(x) = x+3, g(x) = 2/ x+6

4. Determine whether the given function is one-to-one. If so, find it's inverse.
f(x)= 4x-20

Thanks again for anyone's help!!!
• Dec 5th 2008, 12:51 PM
Chop Suey
1. Solve for y in each equation, then inspect the slope of the two lines:
- If they are the same, then they are parallel
- If their product is -1, then they are perpendicular
- If they are not equal and their product is not -1, then they are neither parallel nor perpendicular.

2. Note that $(f \cdot g)(x) = f(x) g(x)$

Plug in $x = 2$ in $f(x)$ and $g(x)$, then find their products.

3. $(f \circ g)(x) = f(g(x)) = \left(\frac{2}{x+6}\right)+3$

The domain is the set of real numbers for which the composite function is defined. The function is defined for all x such that $x+6 \neq 0 \implies x \neq -6$

4. It's a linear function, so it is injective. To check, graph the function and apply the horizontal line test (If the horizontal lines intersect the curve at most one point, then it is one-to-one. Otherwise, it's not injective.)