Let f x -x-1 and g x -12- Then the set of points where gfgx is continuous is

The correct option is A R f(g(x)) =12 1 = 12=h(x) g(h(x)) =12 ...independent of x.Hence g(f(g(x))) is a constant function. ...

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Byju's Answer

Standard XII

Mathematics

Equation of Tangent at a Point (x,y) in Terms of f'(x)

Let f x =x-...

Question

Let $f (x) = x - 1$ and $g (x) = \frac{1}{2}$ . Then the set of points where $g (f (g (x)))$ is continuous is

R

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R - 1

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(- \infty, \infty)

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(- \infty, \infty) - 0, 1

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Solution

The correct option is A $R$
$f (g (x))$
$= \frac{1}{2} - 1$

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

$g (h (x))$

$= \frac{1}{2}$ ...independent of x.

Hence $g (f (g (x)))$ is a constant function.
Therefore it is straight line parallel to x axis and passing through $y = \frac{1}{2}$ .
Thus it is continuous on R.

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Let f(x)=x−1 and g(x)=12. Then the set of points where g(f(g(x))) is continuous is

The correct option is A Rf(g(x))=12−1=−12=h(x)g(h(x))=12 ...independent of x.Hence g(f(g(x))) is a constant function.Therefore it is straight line parallel to x axis and passing through y=12.Thus it is continuous on R.

Let $f (x) = x - 1$ and $g (x) = \frac{1}{2}$ . Then the set of points where $g (f (g (x)))$ is continuous is