SOLUTION: Given f(x) = k(3 - x), find the value of k if f^-1(6) = 1 steps needed also

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Question 1165869: Given f(x) = k(3 - x), find the value of k if f^-1(6) = 1
steps needed also
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given f%28x%29+=+k%283+-+x%29
first inverse f%5E-1%28x%29+
f%28x%29+=+k%283+-+x%29 -> recall that f%28x%29+=+y
y=+k%283+-+x%29 ......swap x and y
x=+k%283+-+y%29............solve for y
x%2Fk=+3+-+y
y=+3+-+x%2Fk......your inverse
f%5E-1%28x%29+=3+-+x%2Fk

if f%5E-1%286%29+=+1, =>means +x=6

1+=3+-+6%2Fk........solve for k
6%2Fk+=3+-+1
6%2Fk+=2
6%2F2+=k
k=3
so,
f%28x%29+=+3%283+-+x%29
f%28x%29+=+9+-+3x

inverse
f%5E-1%28x%29=3+-+x%2F3
check inverse for x=6
f%5E-1%286%29+=3+-+6%2F3
f%5E-1%286%29+=3+-+2
f%5E-1%286%29+=1 ->which is true