SOLUTION: Given f(x) = 1/(x-5) and g(x)= √(x-2) Find (f o g) (18)?

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Question 1205243: Given f(x) = 1/(x-5) and g(x)= √(x-2) Find (f o g) (18)?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Given
+f%28x%29+=+1%2F%28x-5%29

g%28x%29=+sqrt%28x-2%29+

Find (f o g) (18)

first find (f o g) (x)
(f o g) (x)=f%28sqrt%28x-2%29+%29
(f o g) (x)= 1%2F%28sqrt%28x-2%29+-5%29+
(f o g) (x)= 1%2F%28sqrt%28x-2%29+-5%29+

then

(f o g) (18)= 1%2F%28sqrt%2818-2%29+-5%29
(f o g) (18)= 1%2F%28sqrt%2816%29+-5%29+
(f o g) (18)= 1%2F%284+-5%29
(f o g) (18)= 1%2F%28+-1%29+
(f o g) (18)= -1+



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.


                    It can be solved in two lines:


Line  1 :   First calculate   g(18) = sqrt%2818-2%29 = sqrt%2816%29 = 4.

Line  2 :   Next calculate   (fog)(18) = f(g(18)) = f(4) = 1%2F%284-5%29 = 1%2F%28-1%29 = -1.         ANSWER


                    Done,  complete,  solved.