Find the y-intercepts for the function given by:
f(x)= 4/(x+5)-1/(x-4)/2/(x-3)+3/(x+2)
I am stuck
The y axis intercepts are the values of the function when x = 0
4/5 - [(1/-4)] / [(2/-3)] + 3/2
Is it 0,63/50
To find the y-intercepts of a function, you need to determine the value of y when x is equal to 0.
Let's substitute x=0 into the given function f(x):
f(0) = 4/(0+5) - 1/(0-4)/2/(0-3) + 3/(0+2)
We can simplify this expression:
f(0) = 4/5 - 1/-4/2/-3 + 3/2
Before dealing with the fractions, let's simplify the negative exponents in the denominator:
f(0) = 4/5 - 1/-4*2/-3 + 3/2
Next, let's simplify each fraction:
f(0) = 4/5 + 1/8/3 + 3/2
To add the fractions, we need to find a common denominator:
f(0) = 4/5 + 1/8/3 + 3/2
= 4/5 + 1/8 * 3/3 + 3/2
= 4/5 + 3/24 + 36/24
= (4*24 + 3 + 36)/24
= (96 + 3 + 36)/24
= 135/24
This fraction cannot be simplified further. However, we can write it as a mixed number:
f(0) = 135/24 = 5 15/24
Therefore, the y-intercept of f(x) is y = 5 15/24, which means the function intersects the y-axis at the point (0, 5 15/24).