Question:
If f (x) = ax + b and g (x) = cx + d, then f {g (x)} = g {f (x)} is equivalent to
If f (x) = ax + b and g (x) = cx + d, then f {g (x)} = g {f (x)} is equivalent to
Updated On: Jul 6, 2022
- f (a) = g (c)
- f (b) = g (b)
- f (d) = g (b)
- f (c) = g (a)
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The Correct Option is C
Solution and Explanation
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)]
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