If $f, g, h$ be functions defined as follows $f (x) = x + 2, g (x) = 3 x - 1$ and $h (x) = 2 x$ then, which of the following is true:

h o (g o f) = (h o g) o f

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f o (g o h) = (h o g) o f

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g o (h o f) = (h o g) o f

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g o (h o f) = (g o h) o f

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Solution

The correct option is A $h o (g o f) = (h o g) o f$
$f (x) = x + 2$
$g (x) = 3 x - 1$
$h (x) = 2 x$
$\begin{matrix} h o (g \circ f) & = h (g (f (x))) = h (g (x + 2)) = h (3 (x + 2) - 1) = h (3 x + 5) = 2 (3 x + 5) = 6 x + 10 \end{matrix}$
$\begin{matrix} (hog) \circ f & = (h o g) (f (x)) = (h \circ g) (x + 2) = 6 (x + 2) - 2 = 6 x + 12 - 2 = 6 x + 10 \end{matrix}$

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If f,g,h be functions defined as follows f(x)=x+2,g(x)=3x−1 and h(x)=2x then, which of the following is true:

The correct option is A ho(gof)=(hog)off(x)=x+2g(x)=3x−1h(x)=2xho(g∘f)=h(g(f(x)))=h(g(x+2))=h(3(x+2)−1)=h(3x+5)=2(3x+5)=6x+10(hog)∘f=(hog)(f(x))=(h∘g)(x+2)=6(x+2)−2=6x+12−2=6x+10

If $f, g, h$ be functions defined as follows $f (x) = x + 2, g (x) = 3 x - 1$ and $h (x) = 2 x$ then, which of the following is true: