You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Composite Function

Let f :[1,2] ...

Question

Let $f : [1, 2] \to [1, 4] a n d g : [1, 2] \to [2, 7]$ be two continuous bijective functions such that f(1) = 4 and g(2) = 7. Number of solution of the equation f(x) = g(x) in (1, 2) is equal to

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 1
$f : [1, 2] \to [1, 4] g : [1, 2] \to [2, 7] f (1) = 4 g (2) = 7$
$∵$ f(x) and g(x) are bijective functions f(x) is decreasing and g(x) is increasing functions.
$∴$ Two graphs will meet at only one point.

Suggest Corrections

Similar questions

Q. Let

f : [1, 2] \to [1, 4]

and

g : [1, 2] \to [2, 7]

be two consecutive bijective functions such that

f (1) = 4; g (2) = 7

. The number of solutions of the equation

f (x) = g (x)

(1, 2)

Q. Let

f : R \to R

be a continuous odd function, which vanishes exactly at one point and

f (1) = \frac{1}{2}

. Suppose that

F (x) = \int_{- 1}^{x} f (t) d t

for all

x \in [- 1, 2]

and

G (x) = \int_{- 1}^{x} t | f (f (t)) | d t

for all

x \in [- 1, 2]

lim x \to 1 \frac{F (x)}{G (x)} = \frac{1}{14}

, then the value of

f (\frac{1}{2})

Q. Let

f : [- 1, 2] \to [0, \infty)

be a continuous functlon such that

f (x) = f (1 - x)

for all

x \in [- 1, 2]

. Let

R_{1} = \int_{- 1}^{2} x f (x) d x

, and

R_{2}

be the area of the region bounded by

y = f (x)

x = - 1, x = 2

, and the

x

-axis. Then

Q. Let

f : R \to R

be a continuous odd function, which vanishes exactly at one point and

f (1) = \frac{1}{2} .

Suppose that

F (x) = x \int - 1 f (t) d t

for all

x \in [- 1, 2]

and

G (x) = x \int - 1 t | f (f (t)) | d t

for all

x \in [- 1, 2]

. If

lim x \to 1 \frac{F (x)}{G (x)} = \frac{1}{14}

, then the value of

f (\frac{1}{2})

Let f (x) be a function such that f (x) = x - [x], where [x] is the greatest integer less than or equal to x. Then the number of solutions of the equation $f (x) + f (\frac{1}{x}) = 1$ is (are)

Join BYJU'S Learning Program

Let f:[1,2]→[1,4]and g:[1,2]→[2,7] be two continuous bijective functions such that f(1) = 4 and g(2) = 7. Number of solution of the equation f(x) = g(x) in (1, 2) is equal to

The correct option is A 1f:[1,2]→[1,4]g:[1,2]→[2,7]f(1)=4g(2)=7 ∵ f(x) and g(x) are bijective functions f(x) is decreasing and g(x) is increasing functions. ∴ Two graphs will meet at only one point.

Let $f : [1, 2] \to [1, 4] a n d g : [1, 2] \to [2, 7]$ be two continuous bijective functions such that f(1) = 4 and g(2) = 7. Number of solution of the equation f(x) = g(x) in (1, 2) is equal to

The correct option is A 1
$f : [1, 2] \to [1, 4] g : [1, 2] \to [2, 7] f (1) = 4 g (2) = 7$
$∵$ f(x) and g(x) are bijective functions f(x) is decreasing and g(x) is increasing functions.
$∴$ Two graphs will meet at only one point.