Question:
Let $f: N \rightarrow R$ be the function defined by $f(x)=\frac{2 x-1}{2}$ and $g: Q \rightarrow R$ be another function defined by $g(x)=x+2$. Then, $(g \circ f)(3 / 2)$ is
(a) 1
(b) 2
(c) $\frac{7}{2}$
(d) none of these
Solution:
Given: $f(x)=\frac{2 x-1}{2}$ and $g(x)=x+2$
$(g o f)(x)=g(f(x))$
$=g\left(\frac{2 x-1}{2}\right)$
$=\frac{2 x-1}{2}+2$
$=\frac{2 x-1+4}{2}$
$=\frac{2 x+3}{2}$
$(g o f)\left(\frac{3}{2}\right)=\frac{2\left(\frac{3}{2}\right)+3}{2}$
$=\frac{3+3}{2}$
$=\frac{6}{2}$
$=3$
Hence, the correct option is (d).
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