i forgot to post these!
f(x)=9x+4 and listed in interval notation
also:
f(x) x2+14x+40
in interval notation
and:
1/x^2+81 (interval notation)
and:
x+11/x^2-121 (interval notation)
and:
f(x+2)
f(x)=6x^2-x+7
You have listed a lot of functions but have said nothing about what the interval is. Unless you specify an interval for the variable x, there is no specific intervl for f(x). For further discussion, see http://mathforum.org/library/drmath/view/52929.html
To express the functions in interval notation, we need to establish the interval for the variable x. Since you haven't provided any specific interval, I will assume we are working with the entire real number line (-∞, +∞) for each function.
1. f(x) = 9x + 4:
In interval notation, the function f(x) = 9x + 4 for the entire real number line is (-∞, +∞).
2. f(x) = x^2 + 14x + 40:
To determine the interval notation for f(x) = x^2 + 14x + 40, we need to find the x-values where the function is defined. Since this is a quadratic function, it is defined for all real numbers. Hence, the interval notation is (-∞, +∞).
3. f(x) = 1/(x^2 + 81):
This function represents a rational function. However, since you haven't specified any restrictions on the domain, the function is defined for all real numbers. Therefore, the interval notation for f(x) = 1/(x^2 + 81) on the entire real number line is (-∞, +∞).
4. f(x) = (x + 11)/(x^2 - 121):
This function is also a rational function. To determine the interval notation, we need to find the values that make the denominator equal to zero, as those would be excluded from the domain. In this case, the denominator is x^2 - 121, which factors as (x + 11)(x - 11). Therefore, the function is undefined for x = -11 and x = 11. Hence, the interval notation for f(x) = (x + 11)/(x^2 - 121) is (-∞, -11) ∪ (-11, 11) ∪ (11, +∞).
5. f(x + 2) = 6(x + 2)^2 - (x + 2) + 7:
To simplify the function f(x + 2), we substitute (x + 2) for x in original function f(x) = 6x^2 - x + 7. Now, we can simplify the equation by expanding and combining like terms:
f(x + 2) = 6(x + 2)^2 - (x + 2) + 7
= 6(x^2 + 4x + 4) - (x + 2) + 7
= 6x^2 + 24x + 24 - x - 2 + 7
= 6x^2 + 23x + 29
So, the function f(x + 2) is f(x + 2) = 6x^2 + 23x + 29.