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2 years ago

The composition of a function and its inverse is always

Mathematics

2 answers:

rusak2 [61]2 years ago

7 0

Lets try this with an example.

Suppose we have a function $f(x)=2x$ .

Calculate its inverse $f^{-1}(x)=\dfrac{x}{2}$ .

And now just simply try to find the composition,

$f(f^{-1}(x))=f\Big(\dfrac{x}{2}\Big)=2\cdot\dfrac{x}{2}=x$ .

The answer is the composition of a function and its inverse is always function $g(x)=f(f^{-1}(x))=\boxed{x}$ .

Hope this helps.

dusya [7]2 years ago

4 0

Answer: x

Step-by-step explanation:

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2 years ago

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BlackZzzverrR [31]

Answer:

The solution of the given trigonometric equation

$x = \frac{\pi }{6}$

Step-by-step explanation:

Step(i):-

Given

$cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

$cos( 3x - \frac{\pi }{3} ) = cos (\frac{\pi }{6} )$

$3x - \frac{\pi }{3} = \frac{\pi }{6}$

$3x - \frac{\pi }{3 } + \frac{\pi }{3} = \frac{\pi }{6} + \frac{\pi }{3}$

$3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}$

$x = \frac{\pi }{6}$

Step(ii):-

The solution of the given trigonometric equation

$x = \frac{\pi }{6}$

verification :-

$cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

put $x = \frac{\pi }{6}$

$cos( 3(\frac{\pi }{6}) - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

$cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} = \frac{\sqrt{3} }{2}$

Both are equal

∴The solution of the given trigonometric equation

$x = \frac{\pi }{6}$

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2 years ago