Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 10

HARD

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IMPORTANT

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Suppose $f (x) = a x + b$ and $g (x) = b x + a,$ where $a$ and $b$ are positive integers. If $f \{g (20)\} - g \{f (20)\} = 28,$ then which of the following is not possible?

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Important Questions on Functions

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 11

If

f (x)

is an invertible function and

g (x) = 2 f (x) + 5

, then the value of

g^{- 1} (x)

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 12

If

f (x) = \{\begin{cases} - x + 1, & x \leq 0 \\ - {(x - 1)}^{2}, & x \geq 1 \end{cases}

then the number of solution(s) of

f (x) - f^{- 1} (x) = 0

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 1

Let,

f (x + \frac{1}{y}) + f (x - \frac{1}{y}) = 2 f (x) f (\frac{1}{y}) \forall x, y \in R

,

y \neq 0

and

f (0) = 0

then the value of

f (1) + f (2) =

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 2

If

f (x^{2} - 6 x + 6) + f (x^{2} - 4 x + 4) = 2 x \forall x \in R

then

f (- 3) +

f (9) - 5 f (1) =

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 3

If a function

f : R \to R

be such that,

f (x - f (y)) = f (f (y)) +

x f (y) + f (x) - 1

,

\forall x

,

y \in R

, then

f (2) =

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 4

If

f : R \to R

is a function satisfying

f (x + y) = f (x y)

for all

x, y \in R

and

f (\frac{3}{4}) = \frac{3}{4},

then

f (\frac{9}{16}) =

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 5

A function

f : R \to R

satisfies the equation

f (x) f (y) - f (x y)

= x + y \forall x, y \in R

and

f (1) > 0,

then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 6

Let

f

be a function defined from

R^{+} \to R^{+}

. If

{(f (x y))}^{2} = x f^{2} (y)

for all positive numbers

x

and

y

. If

f (2) = 6

, find

f (50) = ?