# Let $f:N\rightarrow R$ be the function defined by $f(x)=\frac{2x-1}{2}\;and\;g:\;Q \rightarrow R$ be another function defined by g(x)=x+2. Then $(g\;o\;f)\frac{3}{2}$ is

$\begin{array}{1 1}(A)\;1 & (B)\;1\\(C)\;\large\frac{7}{2} & (D)\;none\;of\;these.\end{array}$

Toolbox:
• $(gof)(x)=g(f(x))$
$f:N \to R$

$f(x)=\frac{2x-1}{2}$

$g(x)=g: Q \to R$ be

$g(x)=x+2$

$(gof)(x)=(gof)^{3/2}$

$=g(f(3/2))$

But f is defined form $N \to R$

f is not defined for 3/2 hence

'D' option is correct

answered Mar 5, 2013 by