First slide

Functions (XII)

Question

Let $f (x) = a x + b, x \in R, a n d g (x) = x + d, x \in R,$ then $f o g = g o f$ if and only if

Moderate

A

$f (a) = g (c)$
B

$f (d) = g (b)$
C

$f (b) = g (d)$
D

$f (c) = g (a)$

Solution

$f (g (x)) = g (f (x))$ for all $x \in R \Leftrightarrow f (c x + d) = g (a x + b)$
$\Leftrightarrow a (c x + d) + b = c (a x + b) + d \Leftrightarrow a d + b = c b + d$
$\Leftrightarrow f (d) = g (b)$

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