If $f: R \rightarrow R$ is defined by $f(x)=x^2-3 x+2$, find $f(f(x))$.

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LEELADHAR YADAV Asked Aug 28, 2023

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If $f: R \rightarrow R$ defined by $f(x)=\frac{3 x+5}{2}$ is an invertible function, find $f^{-1}$.

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If the fuction $f: R \rightarrow R$ be given by $f(x)=x^2+2$ and $g: R \rightarrow R$ be given by $g(x)=\frac{x}{x-1}, x \neq 1$, find fog and $g$ and hence find fog (2) and gof $(-3)$.

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If $f: R \rightarrow R$ be defined by $f(x)=\left(3-x^3\right)^{4 / 3}$, then find $f(x)$.

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LEELADHAR YADAV Asked Aug 28, 2023

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If the function $f: R \rightarrow R$ is given by $f(x)=x^2+3 x+1$ and $g: R \rightarrow R$ is given by $g(x)=2 x-3$, find (i) fog and (ii) gof.

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Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $f: A \rightarrow B$ defined by $f(x)=\left(\frac{x-2}{x-3}\right)$. Show that $f$ is oo one and onto and hence find $f^{-1}$.

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If the function $f: R \rightarrow R$ be given by $f(x)=x^2+2$ and $g: R \rightarrow R$ be given by $g(x)=\frac{x}{x-1}$, then find $g^{-1}(x)$ and $\mathrm{fog}(x)$

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Let $g: R \rightarrow(0, \pi / 3]$ is defined by $g(x)=\cos ^{-1}\left(\frac{x^2-k}{1+x^2}\right)$. Then find the possible values of ' $k$ ' for which $g$ is surjective.

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Show that the function $f$ in $A=R-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$ is one-one and onto. Hence find $f^{-1}$

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The function $f:[0,3] \rightarrow[1,29]$, defined by $f(x)=2 x^3-15 x^2+36 x+1$, is $(3,-1), 70]$ (A) one-one and onto

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If the function $f(x)=x^3+e^2$ and $g(x)=f^{-1}(x)$, then the value of $g^{\prime}(1)$ is , $(4,-1), 80]$

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Let $f: R \rightarrow R$ be defined as $f(x)=x^4$. Show that $f$ is not one-one.

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Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in R$. Then the set of all $x$ satisfying $(f \circ g \circ g \circ f)(x)=(g \circ g \circ f)(x)$, wheng $(f \circ g)(x)=f(g(x))$, is

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Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^2}$, then $f$ is both one-one and onto when $B$ is the interval :

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Let $y=\left\{n^2: n \in N\right\}$ Consider $f: N \rightarrow y$ as $f(n)=n^2$. Show that $f$ is invertible. Find the inverse of $f$.

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$, where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Show that $f$ is invertible. Find the inverse.

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thedablukumar Asked Jan 13, 2023

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यदि फलन $f: R \rightarrow R$ इस प्रकार परिभाषित है, कि $f(x)=\left(3-x^3\right)^{\frac{1}{3}}$ तो $f o f(x)$ है — —

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If a function is defined as $f(x)=\sqrt{\log _{h(x)} g(x)}$, where $g(x)=|\sin x|+\sin x, h(x)=\sin x+\cos x, 0 \leq x \leq \pi$. Then find the doman of $f(x)$.

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If $\mathrm{f}$ be a greatest integer function and $\mathrm{g}$ be an absolute value function. Find the value of $\text { (log) }\left(\frac{-3}{2}\right)+(\text { gof })\left(\frac{4}{3}\right) \text {. }$

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Its inverse is -

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Let $f$ be a function defined by $f(x)=(x-1)^2+1,(x \geq 1)$.

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Show that ${ }^*: R \times R \rightarrow R$ defined by $a{ }^* b=a+2 b$ is not commutative.

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If $f(x)=x+7$ and $g(x)=x-7, x \in R$, find (fog) (7).

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Find the domain of the function $f(x)=\sqrt{\frac{\log _{\frac{x}{2}}}{2} \log _2 \frac{2 x \quad 1}{3 x}}$

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Let A={1,2,3,4,5,6} and * be an operation A defined by $a{ }^* b=r$, where r is the least non-negative remainder when the product a b is divided by k. Operation * is binary operation if k=

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If $f: R \rightarrow R$ is defined by $f(x)=x^2-3 x+2$, find $f(f(x))$.

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