CameraIcon

CameraIcon

SearchIcon

MyQuestionIcon

MyQuestionIcon

Cartesian Product

If f(g(x)) is...

Question

If f(g(x)) is one one then which of f(x),g(x) is necessary one one? Similarly for onto?

Open in App

Solution

Suggest Corrections

thumbs-up

0

BNAT

mid-banner-image

Similar questions

f (x) = a x + b

g (x) = c x + d

f (g (x)) = g (f (x)),

then which one of the following is correct?

Q. Which of the following statements are incorrect?
I If

f (x)

g (x)

are one to one then

f (x)

g (x)

f (x)

g (x)

are one to one then

f (x) . g (x)

f (x)

is odd then it is necessarily one to one.

f : R \to R

f (x) = 2 x - 1

g : R - {1} \to R

g (x) = \frac{x - \frac{1}{2}}{x - 1}

. Then the composition function

f (g (x))

Q. Which of following statements is/are INCORRECT?
I. If

f (x)

g (x)

are one-one, then

f (x) + g (x)

is also one-one.
II. If

f (x)

g (x)

are one-one, then

f (x) . g (x)

is also one-one.
III. If

f (x)

is odd, then it is necessarily one to one.

\to

R be a function. Define g:R

\to

by g(x) = |f(x)| for all x. Then g is

View More

Explore more

Cartesian Product

Standard XII Mathematics