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

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)

A

f(a) = g(c )

B

f(b) = g(b)

C

f(d) = g(b)

D

f(c ) = g(a)

Text Solution

Verified by Experts

The correct Answer is:
C
f(x) = ax + b
g(x) = cx + d
f(g(x)) = g (f(x))
f(cx + d) = g(ax + b)
a (cx + d) + b = c (ax + b) + d
acx + ad + b = acx + bc + d
ad + b = cb + d
f(d) = g(b)
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