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Byju's Answer

Standard XII

Mathematics

f(x) Transforms to f(-x)

Whenever f -1...

Question

Whenever $f^{- 1} (x)$ exists, to draw the graph of $f^{- 1} (x)$ from f(x), we take the reflection of f(x) about y-axis.

True

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False

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Solution

The correct option is B
False

To draw the graph of $f^{- 1} (x)$ from f(x). We take the reflection of f(x) about the line y = x.

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Similar questions

The inverse function of $f^{- 1} (x), i f f^{- 1} (x) e x i s t s i s f (x)$

Graph of f(x) is given. Draw the graph of f $^{- 1}$ (x)

Q. Assertion :Let f(x) is a bijective function. Then

f (x) = f^{- 1} (x) \Rightarrow f^{- 1} (x) = x

Reason:

f^{- 1} (x) = x \Rightarrow f (x) = f^{- 1} (x)

How many of the following statements are correct?
1. Graph of $- f (x)$ is obtained by taking the reflection of $f (x)$ about x-axis.
2. Graph of $f (- x)$ is obtained by taking the reflection of $f (x)$ about x-axis.

3. Graph of $- f (- x)$ is obtained by taking the mirror image of the graph of $f (x)$ about x-axis and then about y-axis.

___

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

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Whenever f−1(x) exists, to draw the graph of f−1(x) from f(x), we take the reflection of f(x) about y-axis.

The correct option is B False To draw the graph of f−1(x) from f(x). We take the reflection of f(x) about the line y = x.

Whenever $f^{- 1} (x)$ exists, to draw the graph of $f^{- 1} (x)$ from f(x), we take the reflection of f(x) about y-axis.

The correct option is B
False

To draw the graph of $f^{- 1} (x)$ from f(x). We take the reflection of f(x) about the line y = x.