Let fx-x2-x-1 and gx-sin x- Show that f - g - g o f-

Fog #160;x=f #160;g #160;x=fsin #160;x=sin2x+sin #160;x+1and #160;gof #160;x=g #160;f #160;x=g #160;x2+x+1= #160;sin #160;x2+x+1So, #1 ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

Let fx=x2+x+1...

Question

Let f(x) = x² + x + 1 and g(x) = sin x. Show that fog ≠ gof.

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Solution

$(f o g) (x) = f (g (x)) = f (\sin x) = \sin^{2} x + \sin x + 1 and (g o f) (x) = g (f (x)) = g (x^{2} + x + 1) = \sin (x^{2} + x + 1) So, f o g \neq g o f .$

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Similar questions

Q. Let f : R → R and g : R → R be defined by f(x) = x² and g(x) = x + 1. Show that fog ≠ gof.

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Let $f (x) = x^{2}$ and $g (x) = sin x$ for all $x \in R$ . Then the set of all $x$ satifying $(f \circ g \circ g \circ f) (x) = (g \circ g \circ f) (x)$ , where $(f \circ g) (x) = f (g (x))$ , is

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Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.

fog x=f g x=fsin x=sin2x+sin x+1and gof x=g f x=g x2+x+1= sin x2+x+1So, fog≠gof.

Let f(x) = x² + x + 1 and g(x) = sin x. Show that fog ≠ gof.

$(f o g) (x) = f (g (x)) = f (\sin x) = \sin^{2} x + \sin x + 1 and (g o f) (x) = g (f (x)) = g (x^{2} + x + 1) = \sin (x^{2} + x + 1) So, f o g \neq g o f .$