JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

If the function

f\left( x \right)

is defined by

f\left( x \right) = a + bx

and

{f^r} = fff \ldots

(repeated

r

times), then

{f^r}\left( x \right)

is equal to

View answer and explanation

Correct option: D

a\left( {\frac{{{b^r} - 1}}{{b - 1}}} \right) + {b^r}x

Option D,

a\left( {\frac{{{{b^r} - 1}}{{{{b - 1}}}}} \right) + {{b^r}x}

, is correct because it represents the general form of the function f(x) repeated r times, derived by iteratively applying the function to itself.

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