Tube lessons

1)

Let \(f:A\rightarrow B\) and \(g:B\rightarrow C\) be two functions such that \(gof:A\rightarrow C\) is onto and \(g:B\rightarrow C\) is one-one then \(f:A\rightarrow B\) is

one-one
onto
into
many-one

2)

Let \(f(x)=e^{x}\) and \(g(x)=\log_{e}{x}\) where x>0 then

fog=gof
\(fog\neq\) gof
\(fog \subset\) gof
\(gof\subset fog\)

3)

If \(f(x)=(a-x^n)^{\frac{1}{n}}\),a>0,n is a natural number then f(f(x))=

1
n
x
nx

4)

If \(\begin{cases}\frac{|x|}{x} & x\neq 0\\0 & x = 0\end{cases}\) and \(g(x)=1+x-[x]\), then for all x,fog(x)=

x
1
f(x)
g(x)

5)

If \(f(x)=1+x^{\frac{1}{3}}\),and \(g(x)=3-x^{\frac{1}{3}}+x\),then g(1)=

3
5
27
4

Mathematics

Twelve Standard

Test your understanding of this lesson Composition of functions | Illustration-1:-

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