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f(x) Transforms to f(|x|)

The graph of ...

Question

The graph of $f (x) = | | x - 1 | - 1 |$ is

A

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B

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C

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D

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Solution

The correct option is C
We know $y = | x |$ ,

For $y = | x - 1 |$ shifting right by $1$ unit

For $y = | x - 1 | - 1$ shifting down by $1$ unit

Now the graph of $y = | | x - 1 | - 1 |$ is

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Similar questions

The function f is defined by
$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1 - x, & x < 0 1, & x = 0 x + 1, & x > 0 \end{matrix}$ Draw the graph of f(x).

f (x) = 2 x^{2} + 5 x + 1

f (x)

f (x) = a (x + 1) (x - 2) + b (x - 2) (x - 1) + c (x - 1) (x + 1)

for real numbers

a, b, c

a^{2} + b^{2} + c^{2} = - 2

f (x) = ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + a^{2} x & (1 + b^{2}) x & (1 + c^{2}) x (1 + a^{2}) x & 1 + b^{2} x & (1 + c^{2}) x (1 + a^{2}) x & (1 + b^{2}) x & 1 + c^{2} x \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

f (x)

is a polynomial of degree

Q. The graph of the curve

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

f (x) = \frac{1}{1 - x},

x \neq 0, 1,

then the graph of the function

y = f {f (f (x))}, x > 1,

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f(x) Transforms to f(|x|)

Standard XIII Mathematics

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