Properties of Functions and Graphs
Sets, Relation and Function

116866 Let the functions \(f, g, h\) are defined from the set of real numbers \(R\) to \(R\) such that \(f(x)=x^2-1, g(x)=\sqrt{\left(x^2+1\right)}\) and \(h(x)=\left\{\begin{array}{l}0, \text { if } x\lt 0 \\ x, \text { if } x \geq 0,\end{array}\right.\) then ho(fog) (x) is defined by

1 \(x\)
2 \(x^2\)
3 0
4 None of these
Sets, Relation and Function

116867 Let \(f(x)=x-[x]\) for all real number, where [x] is the integral part of \(x\), then \(\int_{-1}^1 f(x) d x\) is equal to:

1 1
2 2
3 0
4 \(1 / 2\)
Sets, Relation and Function

116868 If \(2 f(x)-3 f\left(\frac{1}{x}\right)=x^2, x \neq 0\) then what is \(f(2)\) equal to?

1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{5}{4}\)
4 \(-\frac{7}{4}\)
Sets, Relation and Function

116869 The solution of \(|x-2|\lt 5\) is all the real numbers satisfying

1 \(-2\lt x\lt 5\)
2 \(-3\lt x\lt 7\)
3 \(-5\lt x\lt 7\)
4 \(-3\lt x\lt 5\)
Sets, Relation and Function

116866 Let the functions \(f, g, h\) are defined from the set of real numbers \(R\) to \(R\) such that \(f(x)=x^2-1, g(x)=\sqrt{\left(x^2+1\right)}\) and \(h(x)=\left\{\begin{array}{l}0, \text { if } x\lt 0 \\ x, \text { if } x \geq 0,\end{array}\right.\) then ho(fog) (x) is defined by

1 \(x\)
2 \(x^2\)
3 0
4 None of these
Sets, Relation and Function

116867 Let \(f(x)=x-[x]\) for all real number, where [x] is the integral part of \(x\), then \(\int_{-1}^1 f(x) d x\) is equal to:

1 1
2 2
3 0
4 \(1 / 2\)
Sets, Relation and Function

116868 If \(2 f(x)-3 f\left(\frac{1}{x}\right)=x^2, x \neq 0\) then what is \(f(2)\) equal to?

1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{5}{4}\)
4 \(-\frac{7}{4}\)
Sets, Relation and Function

116869 The solution of \(|x-2|\lt 5\) is all the real numbers satisfying

1 \(-2\lt x\lt 5\)
2 \(-3\lt x\lt 7\)
3 \(-5\lt x\lt 7\)
4 \(-3\lt x\lt 5\)
Sets, Relation and Function

116866 Let the functions \(f, g, h\) are defined from the set of real numbers \(R\) to \(R\) such that \(f(x)=x^2-1, g(x)=\sqrt{\left(x^2+1\right)}\) and \(h(x)=\left\{\begin{array}{l}0, \text { if } x\lt 0 \\ x, \text { if } x \geq 0,\end{array}\right.\) then ho(fog) (x) is defined by

1 \(x\)
2 \(x^2\)
3 0
4 None of these
Sets, Relation and Function

116867 Let \(f(x)=x-[x]\) for all real number, where [x] is the integral part of \(x\), then \(\int_{-1}^1 f(x) d x\) is equal to:

1 1
2 2
3 0
4 \(1 / 2\)
Sets, Relation and Function

116868 If \(2 f(x)-3 f\left(\frac{1}{x}\right)=x^2, x \neq 0\) then what is \(f(2)\) equal to?

1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{5}{4}\)
4 \(-\frac{7}{4}\)
Sets, Relation and Function

116869 The solution of \(|x-2|\lt 5\) is all the real numbers satisfying

1 \(-2\lt x\lt 5\)
2 \(-3\lt x\lt 7\)
3 \(-5\lt x\lt 7\)
4 \(-3\lt x\lt 5\)
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Sets, Relation and Function

116866 Let the functions \(f, g, h\) are defined from the set of real numbers \(R\) to \(R\) such that \(f(x)=x^2-1, g(x)=\sqrt{\left(x^2+1\right)}\) and \(h(x)=\left\{\begin{array}{l}0, \text { if } x\lt 0 \\ x, \text { if } x \geq 0,\end{array}\right.\) then ho(fog) (x) is defined by

1 \(x\)
2 \(x^2\)
3 0
4 None of these
Sets, Relation and Function

116867 Let \(f(x)=x-[x]\) for all real number, where [x] is the integral part of \(x\), then \(\int_{-1}^1 f(x) d x\) is equal to:

1 1
2 2
3 0
4 \(1 / 2\)
Sets, Relation and Function

116868 If \(2 f(x)-3 f\left(\frac{1}{x}\right)=x^2, x \neq 0\) then what is \(f(2)\) equal to?

1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{5}{4}\)
4 \(-\frac{7}{4}\)
Sets, Relation and Function

116869 The solution of \(|x-2|\lt 5\) is all the real numbers satisfying

1 \(-2\lt x\lt 5\)
2 \(-3\lt x\lt 7\)
3 \(-5\lt x\lt 7\)
4 \(-3\lt x\lt 5\)