HARD
JEE Main/Advance
IMPORTANT
Earn 100

If f(x)=-1+|x-1|,-1x3;g(x)=2-|x+1|,-2x2, then calculate (fog)x & (gof)(x). Draw their graph. Discuss the continuity of (fog)x at x=-1 & the differentiability of (gof)x at x=1.

Important Questions on Functions

MEDIUM
JEE Main/Advance
IMPORTANT
Let f(x) be a real value function not identically zero satisfies the equation,
fx+yn=f(x)+(f(y))n for all realx&y and f'(0)0 where n(>1) is an odd natural number. Find f(10)
HARD
JEE Main/Advance
IMPORTANT
Solve : log-x2-6x10sin x+sin 3x=log-x2-6x10sin 2x.
HARD
JEE Main/Advance
IMPORTANT

Find the domain of definition the following function.

(Read the symbol · as fractional part function respectively)

fx=1-sinxlog51-4x2+cos-11-x

EASY
JEE Main/Advance
IMPORTANT

The graph of a function f is given.

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State the value of f-1.

EASY
JEE Main/Advance
IMPORTANT

The graph of a function f is given.

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For what values of x is fx=2

EASY
JEE Main/Advance
IMPORTANT

The graph of a function f is given.

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State the domain and range of f.

EASY
JEE Main/Advance
IMPORTANT

The graph of a function f is given.

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Estimated value of f2 is-

EASY
JEE Main/Advance
IMPORTANT

The graph of a function f is given.

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Estimated value of x such that fx=0, is