Leadership

Mathematics

Twelve Standard

Test your understanding of this lesson Composition of functions | composite function theorem and properties of composite function:-

1)
The functions\(f,g:R\rightarrow R\) defined by f(x)=2x and g(x)=sinx.Then (f+g)(x) is
  • one-one and onto
  • one-one but not onto
  • onto but not one-one
  • neither one-one nor onto
2)
Let f(x)=[x] and g(x)=x-[x];then
  • (f+g)(x)=x
  • (fog)(x)=0
  • (gof)(x)=0
  • all are true
3)
Let \(f,g:R\rightarrow R\) defined by f(x)=\({x}^{2}\) and g(x)=\(\sqrt{x}\); then
  • (fog)(4)=3
  • (gof)(-2)=2
  • (fog)(256)=8
  • (gof)(16)=2
4)
If \(f(x)=x^2-1\), g(x)=2x+3 and \(h(x)=(x+1)^{-1}\),then ((fog)oh)(x)=
  • \(\frac{8x^2+28x+24}{x+1}\)
  • \(\frac{8x^2+28x+4}{(x+1)^2}\)
  • \(\frac{8x^2+28x+24}{x+1)^2}\)
  • \(\frac{8x^2+28x+24}{x-1}\)
5)
Let f(x)=\(x^3-x\) and g(x)=sin 2x;then (fog)\(\Big(\frac{\pi}{12}\Big)\)=
  • \(\frac{\3}{8}\)
  • \(\frac{\-3}{4}\)
  • \(\frac{\-3}{8}\)
  • \(\frac{\3}{4}\)
Hand draw

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