MyQuestionIcon

1

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

How to Find the Inverse of a Function

If : A→B and ...

Question

If : A→B and g : B →C be two functions. Then, composition of f and g, gof : A→C is defined as

A

(gof)(x) = f(x), for all x ∈ A

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

B

(gof)(x) = g(f(x)), for all x ∈ A

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

C

(gof)(x) = f(g(x)), for all x ∈ A

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

D

(gof)(x) = g(x), for all x ∈ A

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

Open in App

Solution

The correct option is B
(gof)(x) = g(f(x)), for all x ∈ A

By definition, composition of f and g, gof is defined as (gof)(x) = g(f(x)), for all x ϵ A.

Suggest Corrections

thumbs-up

4

Similar questions

f : X \to Y

g : Y \to X

be two functions such that

(g o f) (x) = x

x ϵ X

f (x) = a x + b and g (x) = c x + d, a \neq 0, c \neq 0.

a = 1, b = 2,

(f o g) (x) = (g o f) (x)

x

what can you say about c and d _________________.

f (x) = \frac{x + 2}{5}

gof (x) = x - 3

g

.

Q. Assertion :If

f (x) = s g n (x)

g (x) = x (1 - x^{2}),

f o g (x)

g o f (x)

are continuous everywhere Reason:

f o g (x) = ⎧ ⎨ ⎩ \begin{matrix} \begin{matrix} - 1, & x \in (- 1, 0) \cup (1, \infty) \end{matrix} \begin{matrix} 0, \end{matrix} x \in {- 1, 0, 1} \begin{matrix} 1, & x \in (- \infty, - 1) \cup (0, 1) \end{matrix} \end{matrix}

g o f (x) = 0, \forall x \in R

f (x) = x | x |, g (x) = sin x

h (x) = (g o f) (x)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Inverse of a Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

How to Find the Inverse of a Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon