f(x)=sqrt(x+4)+sqrt(4-x)
Find X and Y intercepts
To find the x-intercepts of the function f(x), we set f(x) equal to zero and solve for x.
So, let's set f(x) = 0:
sqrt(x+4) + sqrt(4-x) = 0
Now, let's square both sides of the equation to eliminate the square roots:
(x+4) + 2(sqrt(x+4))(sqrt(4-x)) + (4-x) = 0
Simplifying this equation gives:
2(sqrt(x+4))(sqrt(4-x)) = -8
Dividing both sides by 2:
(sqrt(x+4))(sqrt(4-x)) = -4
Now, square both sides again:
(x+4)(4-x) = (-4)^2
Simplifying and expanding:
4x - x^2 + 16 - 4x = 16
Combining like terms:
-x^2 + 4x = 0
Factoring out -x:
x(-x + 4) = 0
So, we have two possible solutions:
x = 0 or -x + 4 = 0
x = 4
Therefore, the x-intercepts of the function f(x) are x = 0 and x = 4.
To find the y-intercept, we set x = 0 and solve for f(x):
f(0) = sqrt(0+4) + sqrt(4-0)
= sqrt(4) + sqrt(4)
= 2 + 2
= 4
Therefore, the y-intercept of the function f(x) is y = 4.