The graph of the function y - f x is symmetrical about the line x -2- thenA- f x -2- f x -2B- f2-x-f2-xC- fx-f-xD- fx-f-x

The correct option is B f (2 + x) =f (2 x)As nbsp;the nbsp;graph nbsp;of nbsp;f nbsp;is nbsp;symmetrical nbsp;about nbsp;x=2,the nbsp;graph ...

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

Byju's Answer

Standard X

Mathematics

Properties of Periodic Function

The graph of ...

Question

The graph of the function y = f(x) is symmetrical about the line x = 2, then

f ( x+2) = f (x - 2)

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

f (2 + x) =f (2 - x)

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

f(x) = f(-x)

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

f(x) = - f(-x)

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

Open in App

Solution

The correct option is B f (2 + x) =f (2 - x)
$As the graph of f is symmetrical about x = 2, the graph of f to the left of x = 2 is same as the graph of f to the right of x = 2 . \Rightarrow If (2 - x, y) is a point on the graph, then (2 + x, y) is also a point on the graph . \Rightarrow The functional value at (2 - x) is same as that of functional value at (2 + x) . \Rightarrow f (2 + x) = f (2 - x)$

Suggest Corrections

Similar questions

Q. The graph of the function

y = f (x)

is symmetrical about line

x = 2,

then

The graph of the function $y = f (x)$ is symmertical about the line $x = 2$ , then

Q. If

f : R \to R

is an invertible function such that

f (x)

and

f^{- 1} x

are symmetric about the line

y = - x

, then

Q. Let

f (x)

be one-one and onto function, such that

| f (x) - f^{- 1} (x) | > 0

for

x ϵ (0, 2) \cup (2, 4)

given

f (2) = 2, f (4) = 0

and

f (0) = 4

. Let

g (x) = \sqrt{16 - x^{2}}

. Given

f (x) < g (x) \forall x ϵ (0, 4)

and graph of

y = f (x)

and

y = f^{- 1} (x)

are symmetrical about the line

x + y = 4

.

If

f (x) - f^{- 1} (x) < 0

for

x ϵ (0, 2)

and

\int_{0}^{2} f (x) d x = 5

, then

\int_{2}^{4} f^{- 1} (x) d x

Q. Let

f (x)

be one-one and onto function, such that

| f (x) - f^{- 1} (x) | > 0

for

x ϵ (0, 2) \cup (2, 4)

given

f (2) = 2, f (4) = 0

and

f (0) = 4

. Let

g (x) = \sqrt{16 - x^{2}}

. Given

f (x) < g (x) \forall x ϵ (0, 4)

and graph of

y = f (x)

and

y = f^{- 1} (x)

are symmetrical about the line

x + y = 4

.

If

f (x) - f^{- 1} (x) > 0

for

x ϵ (0, 2)

and

\int_{0}^{2} (f (x) - f^{- 1} (x)) d x = 2, \int_{2}^{4} f^{- 1} (x) d x = 3

, then

\int_{0}^{4} [g (x) - m a x (f (x), f^{- 1} (x))] d x

Join BYJU'S Learning Program