f(x) = 3x^2-5 and g(x) = 2/x. find the function of f(g(x)) and give the domain.
Solve equation with exact answers: -x^2-3x+10 = 0
f(x) = ln(4-x) find the domain
Help appreciated
Thanks!
1) Substitute the x in f by the term of g:
$\displaystyle f(x)=3\cdot \left(\dfrac2x\right)^2-5 = \dfrac{12}{x^2}-5$
Since the division by zero is not allowed the domain is $\displaystyle D=\mathbb{R}\setminus \{0\}$
2) $\displaystyle -x^2-3x+10 = 0$
Use the quadratic formula to solve this equation. I've got $\displaystyle x = -5~\vee~x = 2$
3) You are supposed to know that the ln-function is defined for positive arguments only. Thus the domain is $\displaystyle D = \{ x | 4-x > 0\}_{ \mathbb{R}}$