CameraIcon

SearchIcon

MyQuestionIcon

1

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

Inverse of a Function

f:Q→ Q is def...

Question

$f : Q \to Q$ is defined by $f (x) = 15 x + 7$ is

A

injective only

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

B

surjective only

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

C

bijective

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

D

neither injective nor surjective

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

Open in App

Solution

The correct option is D bijective
$y = 15 x + 7$ is a linear function.
Since linear functions are bijective, ie. there is only one value of $y$ corresponding to a single value of $x$ , hence $f (x)$ is bijective and invertible.
$x = \frac{y - 7}{15}$
Hence, option 'C' is correct.

Suggest Corrections

thumbs-up

0

Similar questions

f : N \to N

is a function defined as

f (x) = 3 x^{2} + 2.

f (x)

Q. Let a function

f : (0, \infty) \to (0, \infty)

f (x) = ∣ ∣ ∣ 1 - \frac{1}{x} ∣ ∣ ∣

f

Q. Classify the following functions as injection, surjection or bijection :
(i) f : N → N given by f(x) = x²
(ii) f : Z → Z given by f(x) = x²
(iii) f : N → N given by f(x) = x³
(iv) f : Z → Z given by f(x) = x³
(v) f : R → R, defined by f(x) = |x|
(vi) f : Z → Z, defined by f(x) = x² + x
(vii) f : Z → Z, defined by f(x) = x − 5
(viii) f : R → R, defined by f(x) = sinx
(ix) f : R → R, defined by f(x) = x³ + 1
(x) f : R → R, defined by f(x) = x³ − x
(xi) f : R → R, defined by f(x) = sin²x + cos²x
(xii) f : Q − {3} → Q, defined by

f (x) = \frac{2 x + 3}{x - 3}

(xiii) f : Q → Q, defined by f(x) = x³ + 1
(xiv) f : R → R, defined by f(x) = 5x³ + 4
(xv) f : R → R, defined by f(x) = 3 − 4x
(xvi) f : R → R, defined by f(x) = 1 + x²
(xvii) f : R → R, defined by f(x) =

\frac{x}{x^{2} + 1}

[NCERT EXEMPLAR]

Q. Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f⁻¹

Q. The function :

R \to [- \frac{1}{2}, \frac{1}{2}]

f (x) = \frac{x}{1 + x^{2}}

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

Inverse of a Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon