If $f (x) = ax+b$ and $g(x) = cx + d$, t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f (x) = ax+b$ and $g(x) = cx + d$, then $f (g(x)) = g( f (x))$ if

Options:

$f (a) = g(c)$

$f (b) = g(x)$

$f (d) = g(b)$

$f (c) = g(a)$

Correct Answer:

$f (d) = g(b)$

Explanation:

$f (g(x)) = ag(x)+ b = a(cx + d)+ b = acx + ad +b$

$g( f (x)) = cf (x)+ d = c(ax +b)+ d = acx +bc + d$

$∴ f (g(x)) = g( f (x))$ if $ad + b = bc + d$

i.e. if $f (d) = g(b)$