If f(x-2)= square root of x^2 - 16 and g(x)= 3^x/(2-x), then find [f(3)+g(5)]/2.
I honestly don`t even know where to start! please help :[
To find the value of [f(3)+g(5)]/2, we need to first substitute the values of x = 3 and x = 5 into the given functions f(x) and g(x), respectively.
Let's start with f(x-2) = √(x^2 - 16). In this case, we want to find f(3). So, substitute x = 3 into f(x-2):
f(3-2) = √(3^2 - 16)
f(1) = √(9 - 16)
f(1) = √(-7)
Since the value under the square root is negative, we cannot find the square root of -7, which means f(1) is undefined in this case.
Moving on to g(x) = 3^x/(2-x). Now, we need to find g(5). So, substitute x = 5 into g(x):
g(5) = 3^5 / (2-5)
g(5) = 243 / -3
g(5) = -81
Now, we have f(1) as undefined and g(5) as -81.
Finally, substitute these values into the expression [f(3)+g(5)]/2:
[f(3)+g(5)]/2 = [undefined + (-81)]/2
Since we have an undefined value, we cannot proceed any further, and the final answer becomes undefined as well.