117023 For a suitable chosen real constant a, let a function \(\mathbf{f}: \mathbf{R}-\{\mathbf{a}\} \rightarrow \mathbf{R}\) be defined by \(\mathbf{f}(\mathbf{x})=\) \(\frac{a-x}{a+x}\). Further suppose that for any real number \(x \neq-a\) and \(f(x) \neq-a\), (fof)( \(x)=x\).
Then, \(f\left(-\frac{1}{2}\right)\) is equal to

117025 If \(f(x)=\log \left(\frac{1+x}{1-x}\right),-1\lt x\lt 1\), then \(f\left(\frac{3 \mathrm{x}+\mathrm{x}^3}{1+3 \mathrm{x}^2}\right)-f\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^2}\right)\) is

117026 \(\log _2\left(9-2^x\right)=10^{\log (3-x),}\) solve for \(x\).

117027 The number of positive integral solutions of \(x^2+9\lt (x+3)^2\lt 8 x+25\), is

117028 The greatest value of the function \(f(x)=\mathrm{xe}^{-\mathrm{x}}\) in \([0, \infty)\), is

117023 For a suitable chosen real constant a, let a function \(\mathbf{f}: \mathbf{R}-\{\mathbf{a}\} \rightarrow \mathbf{R}\) be defined by \(\mathbf{f}(\mathbf{x})=\) \(\frac{a-x}{a+x}\). Further suppose that for any real number \(x \neq-a\) and \(f(x) \neq-a\), (fof)( \(x)=x\).
Then, \(f\left(-\frac{1}{2}\right)\) is equal to

117025 If \(f(x)=\log \left(\frac{1+x}{1-x}\right),-1\lt x\lt 1\), then \(f\left(\frac{3 \mathrm{x}+\mathrm{x}^3}{1+3 \mathrm{x}^2}\right)-f\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^2}\right)\) is

117026 \(\log _2\left(9-2^x\right)=10^{\log (3-x),}\) solve for \(x\).

117027 The number of positive integral solutions of \(x^2+9\lt (x+3)^2\lt 8 x+25\), is

117028 The greatest value of the function \(f(x)=\mathrm{xe}^{-\mathrm{x}}\) in \([0, \infty)\), is

117023 For a suitable chosen real constant a, let a function \(\mathbf{f}: \mathbf{R}-\{\mathbf{a}\} \rightarrow \mathbf{R}\) be defined by \(\mathbf{f}(\mathbf{x})=\) \(\frac{a-x}{a+x}\). Further suppose that for any real number \(x \neq-a\) and \(f(x) \neq-a\), (fof)( \(x)=x\).
Then, \(f\left(-\frac{1}{2}\right)\) is equal to

117025 If \(f(x)=\log \left(\frac{1+x}{1-x}\right),-1\lt x\lt 1\), then \(f\left(\frac{3 \mathrm{x}+\mathrm{x}^3}{1+3 \mathrm{x}^2}\right)-f\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^2}\right)\) is

117026 \(\log _2\left(9-2^x\right)=10^{\log (3-x),}\) solve for \(x\).

117027 The number of positive integral solutions of \(x^2+9\lt (x+3)^2\lt 8 x+25\), is

117028 The greatest value of the function \(f(x)=\mathrm{xe}^{-\mathrm{x}}\) in \([0, \infty)\), is

117023 For a suitable chosen real constant a, let a function \(\mathbf{f}: \mathbf{R}-\{\mathbf{a}\} \rightarrow \mathbf{R}\) be defined by \(\mathbf{f}(\mathbf{x})=\) \(\frac{a-x}{a+x}\). Further suppose that for any real number \(x \neq-a\) and \(f(x) \neq-a\), (fof)( \(x)=x\).
Then, \(f\left(-\frac{1}{2}\right)\) is equal to

117025 If \(f(x)=\log \left(\frac{1+x}{1-x}\right),-1\lt x\lt 1\), then \(f\left(\frac{3 \mathrm{x}+\mathrm{x}^3}{1+3 \mathrm{x}^2}\right)-f\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^2}\right)\) is

117026 \(\log _2\left(9-2^x\right)=10^{\log (3-x),}\) solve for \(x\).

117027 The number of positive integral solutions of \(x^2+9\lt (x+3)^2\lt 8 x+25\), is

117028 The greatest value of the function \(f(x)=\mathrm{xe}^{-\mathrm{x}}\) in \([0, \infty)\), is

117023 For a suitable chosen real constant a, let a function \(\mathbf{f}: \mathbf{R}-\{\mathbf{a}\} \rightarrow \mathbf{R}\) be defined by \(\mathbf{f}(\mathbf{x})=\) \(\frac{a-x}{a+x}\). Further suppose that for any real number \(x \neq-a\) and \(f(x) \neq-a\), (fof)( \(x)=x\).
Then, \(f\left(-\frac{1}{2}\right)\) is equal to

117025 If \(f(x)=\log \left(\frac{1+x}{1-x}\right),-1\lt x\lt 1\), then \(f\left(\frac{3 \mathrm{x}+\mathrm{x}^3}{1+3 \mathrm{x}^2}\right)-f\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^2}\right)\) is

117026 \(\log _2\left(9-2^x\right)=10^{\log (3-x),}\) solve for \(x\).

117027 The number of positive integral solutions of \(x^2+9\lt (x+3)^2\lt 8 x+25\), is

117028 The greatest value of the function \(f(x)=\mathrm{xe}^{-\mathrm{x}}\) in \([0, \infty)\), is