Determine f(3) if f(3x)+3*f(-3x)=x+1

Expert Answers

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

We have to find f(3) given that f(3x) + 3*f(-3x) = x + 1

f(3x) + 3*f(-3x) = x + 1

for x = 1

=> f(3) + 3*f(-3) = 1 + 1 = 2 ...(1)

for x = -1

=> f(-3) + 3*f(3) = 0 ...(2)

(1) - 3*(2)

=> f(3) + 3*f(-3) - 3*f(-3) - 9*f(3) = 2

=> f(3) - 9*f(3) = 2

=> -8*f(3) = 2

=> f(3) = -1/4

The required value of f(3) = -1/4

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial