SOLUTION: For each of the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = sqrt{x-5}

Algebra ->  Functions -> SOLUTION: For each of the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = sqrt{x-5}       Log On


   

Question 1177905: For each of the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain:
f(x) = sqrt{x-5}
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+sqrt%28x-5%29

if f’ >0 the function is increasing
if f’ <0 the function is increasing
f’%28x%29+=+1%2F%282+sqrt%28x+-+5%29%29
f’ >0 for x%3E5
f’ <0-> no solution in x element R
the function is increasing 5%3Cx%3Cinfinity

A function is even if f%28-x%29=f%28x%29 for all x element R.
f%28-x%29=f%28x%29+
+sqrt%28-x-5%29=sqrt%28x-5%29
-x-5%3C%3E++x-5=> A function is noteven
A function is odd if f%28-x%29=-f%28x%29 for all x element R.
f%28-x%29=f%28x%29+
sqrt%28-x-5%29=-+sqrt%28x-5%29
-x-5%3C%3E+-%28x-5%29
-x-5%3C%3E+-x%2B5=> A function is notodd
so, your function is neither+even+nor+odd

If y+=+f+%28x%29, then the inverse relation is written as y+=+f+%5E-1%28x%29.
If+the inverse is also a function, then we say that the function f is invertible.
f%28x%29+=+sqrt%28x-5%29...find inverse
f%28x%29+=+y
y+=+sqrt%28x-5%29....swap x and y
x+=+sqrt%28y-5%29........solve for y, square both sides
x%5E2+=y-5
x%5E2%2B5+=y
f+%5E-1%28x%29=x%5E2%2B5 which is also a function
so, f%28x%29+=+sqrt%28x-5%29 is invertible on its natural domain