What is x if f(x)=2x^2-1 and g(x)=x-1 if fog=0

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have f(x)=2x^2-1 and g(x)= x-1,

fog(x )= f(g(x))

= f( x-1)

= 2(x-1)^2 - 1

=> 2*(x^2 + 1 - 2x) - 1

=> 2x^2 + 2 - 4x - 1

=> 2x^2 - 4x + 1

As fog(x ) = 0

=> 2x^2 - 4x + 1 =...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

We have f(x)=2x^2-1 and g(x)= x-1,

fog(x )= f(g(x))

= f( x-1)

= 2(x-1)^2 - 1

=> 2*(x^2 + 1 - 2x) - 1

=> 2x^2 + 2 - 4x - 1

=> 2x^2 - 4x + 1

As fog(x ) = 0

=> 2x^2 - 4x + 1 = 0

x1 = [ -b + sqrt (b^2 - 4ac)]/2a

=> x1 = [ 4 + sqrt (16 - 8)]/4

=> x1 = 1 + sqrt 8/4

x2 = 1 - sqrt 8 / 4

So x = 1 + sqrt 8/4 and x = 1 - sqrt 8 / 4

Approved by eNotes Editorial Team