find the domain of
(x-2)/(-3x+7)
all reals except where -3x+7=0.
thank you so much steve!!
could you help me with this one?
Let
f(x) = square root (x + 2)
and
g(x) = x^2 − 2.
Determine the domain of the composite function. (Enter your answer using interval notation.)
f compose f
_____?
and Find the composite function.
(f compose f)(x) = ___?
f(f) = √(f+2) = √(√(x+2)+2)
Sure you didn't want
f(g) = √(x^2-2+2) = |x|
or g(f) = (x+2)-2 = x
?
no sir, it asks for f(f).
now all I need help on is finding the domain of the f(f) that you just posted.
Thanks, I finally got it.
To find the domain of a rational function, such as (x-2)/(-3x+7), we need to determine the values of x for which the function is defined. In other words, we need to find the numbers that we can substitute into the function without causing any division by zero.
In this case, the function is defined as long as the denominator (-3x+7) is not equal to zero. Division by zero is undefined in mathematics.
To solve -3x+7 ≠ 0, we isolate x:
-3x+7 ≠ 0
-3x ≠ -7
x ≠ (-7)/(-3)
x ≠ 7/3
Therefore, x cannot be equal to 7/3 because it would make the denominator zero.
The domain of the function (x-2)/(-3x+7) is all real numbers except x = 7/3.