If f(x) = ax + b and g(x) = cx + d, then f(g(x)) = g(f(x)) is equ… - Vidyadip

MCQ

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
$f(b) = g(b)$
✓
$f(d) = g(b)$
D
$f(c) = g(a)$

✓

Answer

Correct option: C.

$f(d) = g(b)$

c
(c) We have $f(x) = ax + b,\,g(x) = cx + d$ and $f(g(x)) = g(f(x))$

==> $f(cx + d) = g(ax + b)$

==> $a[cx + d] + b = c[ax + b] + d$

==> $ad + b = cb + d$==> $f(d) = g(b)$.

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