Given that f(x)=1/(sqr(1-x) and f(a)=2, waht is the value of f(1-a)?

Question

This is part of the logarithm chapter.

 

How to get 2/√3 as the answer?

Answer 1

Solve for a when f(a)=2=1/(sqr(1-a)) Multiply both sides of the equation by sqr(1-a). Thsi implies,

 

2sqr(1-a)=1 Square both sides.

 

4(1-a)=1

   4-4a=1

  -4      -4

 

-4a=-3  a=3/4

 

f(1-a)=1/sqr(1-(1-a))=1/sqr(1-1+a)=1/sqr(a)=1/sqr(3/4)=1/√3/2=2/√3

 

Edward, it is good to get into the habit to get rid of the radical in the denominator of the fraction. Multiply both the numerator and denominator by √3 in which is.

 

2/√3*√3/√3=2√3/3=2/3*√3. Note: 2/3*√3 seems easier to see the answer then 2/√3.

 

Answer 2

You can put in 2 for the left side and put in x=a on the right side and then solve for "a." Hopefully you can then simplify that and find that 1-a=1/4. So then put 1/4 back in for "x":

 

f(1-a) = 1/sqrt(1-1/4)

f(1-a) = 1/sqrt(3/4)

f(1-a) = 1/[sqrt(3)/sqrt(4)]

f(1-a) = 1/sqrt(3)/2]

f(1-a) = 2/sqrt(3)

 

Hope that helps!