Consumption function expresses the relationship between consumption and–

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LEELADHAR YADAV Asked Sep 25, 2023

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According to Kenz, consumption function shows relation between?

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The equivalent conductance of NaCl at concentration C and at infinite dilution are $\lambda_C$ and $\lambda_{\infty}$, respectively. The correct relationship between $\lambda_C$ and $\lambda_{\infty}$ is given as (where, the constant B is positive)

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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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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 $f: R \rightarrow R$ 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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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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If $g$ is the inverse of a function $f$ and $f^{\prime}(x)=\frac{1}{1+x^5}$, then $g^{\prime}(x)$ equal to:

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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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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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Suppose $X$ and $Y$ are two sets and $f: X \rightarrow Y$ is a function. For a subset $A$ of $X$, define $f(A)$ to be the subset $\{f(a): a \in A\}$ of $Y$. For a subset $B$ of $Y$, define $f^{-1}(B)$ to be the subset $\{x \in X: f(x) \in B\}$ of $X$.

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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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