f-R-R-f-3x-1-x-5-Find-f-x-

Question Number 198431 by hardmath last updated on 19/Oct/23

f : R \to R

f (3 x - 1) = x + 5

Find : f (x) = ?

Answered by AST last updated on 20/Oct/23

f [3 (\frac{x}{3} + \frac{1}{3}) - 1] = \frac{x + 1}{3} + 5 \Rightarrow f (x) = \frac{x + 16}{3}

Commented by Frix last updated on 20/Oct/23

f (3 (\frac{x}{3} + \frac{1}{3}) - 1) = \frac{x + 1}{3} + 5 = \frac{x + 16}{3}

Commented by AST last updated on 20/Oct/23

✓

Answered by Rasheed.Sindhi last updated on 20/Oct/23

f (3 x - 1) = x + 5; f (x) = ?

L e t 3 x - 1 = y \Rightarrow x = \frac{y + 1}{3}

f (y) = \frac{y + 1}{3} + 5 = \frac{y + 16}{3}

R e p l a c i n g y b y x :

f (x) = \frac{x + 16}{3}

Answered by Rasheed.Sindhi last updated on 20/Oct/23

f (3 x - 1) = x + 5 = \frac{1}{3} (3 x + 15)

= \frac{1}{3} (3 x - 1 + 16)

f (x) = \frac{1}{3} (x + 16)

Commented by hardmath last updated on 20/Oct/23

thank you professors