Question

If f (x) = ax + b and g (x) = cx + d, then f {g (x)} = g {f (x)} is equivalent to

• A. f (a) = g (c)
• B. f (b) = g (b)
• C. f (d) = g (b)
• D. f (c) = g (a)

Answer 1

Answer: (C)

f (d) = g (b)

Answer 2

f (x) = ax + b and g (x) = cx + d f {g (x)}= a (cx + d) + b = acx + ad + b g {f (x)}= c (ax + b) + d = acx + bc + d. since f {g (x)} = g {f (x)} $\Rightarrow$ acx + ad + b = acx + bc + d $\Rightarrow$ ad + b = c . b + d $\Rightarrow$ f (d) = g (b) [$\because$ ad + b = f (d) and bc + d = g (b)]