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Functions

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are (f(x)=x^2), (g(x)=x+1), what is ((f\circ g)(x)-(g\circ f)(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{-3}\to\mathbb{R}\setminus{2}) is given by (f(x)=\frac{2x-1}{x+3}), which statement about (f) is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is considered as (f(x)=\frac{2x-1}{x+3}), which value must be removed from the domain to make it a function?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=mx^2+1), which value of (m) can make (f) one-one on all of (\mathbb{R})?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2+px+q) and its minimum value is (5) at (x=2), what are (p,q)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:(0,\infty)\to\mathbb{R}) is given by (f(x)=x+\frac{1}{x}), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is described by (f(x)=x+\frac{1}{x}), what should be the correct domain?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is an odd function and (g:\mathbb{R}\to\mathbb{R}) is an even function, which statement about (g\circ f) is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:[0,\infty)\to\mathbb{R}) is given by (f(x)=x^2+2x), which statement about its range and one-one behaviour is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}x+2,&x\geq0\x^2+2,&x<0\end{cases}), which statement about (f) being one-one is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (A) has (5) elements and (B) has (3) elements, how many functions from (A) to (B) have range exactly of size (2)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2}{1+x^2}), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=|x-1|+|x+1|), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2-6x+11), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax+b) and (f\circ f) is the identity function, which statement about (a,b) is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}) is given by (f(x)=\frac{3x+1}{x-2}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3+x+5), which statement about (f) is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^3-3x+1), which statement about (f) being one-one is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{N}\to\mathbb{N}) is defined by (f(n)=n+1), where (\mathbb{N}={1,2,3,\ldots}), what type of function is (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) and (g:B\to C) are both invertible functions, then ((g\circ f)^{-1}) is equal to which expression?Class 12Relations and FunctionsFunctionsHard