Chapter 2: Q. 27 (page 100)

If $f (x) = \{\begin{cases} 2 x - 4 i f - 1 \leq x \leq 2 \\ x^{3} - 2 i f 2 < x \leq 3 \end{cases}$
Find: (a) $f (0)$ (b) $f (1)$ (c) $f (2)$ (d) $f (3)$

Short Answer

Expert verified

(a) $- 4$

(b) $- 2$

(d) $25$

Step by step solution

Step 1.Given information

The given function $f (x) = \{\begin{cases} 2 x - 4 i f - 1 \leq x \leq 2 \\ x^{3} - 2 i f 2 < x \leq 3 \end{cases}$

Step 2.Find the value of f(0)

When $x = 0$ , the equation for is given by $f (x) = 2 x - 4$ .

Replace $x$ with $0$ in the function and simplify

$f (0) = 2 (0) - 4 = - 4$

Therefore,the value of $f (0) = - 4$ .

Step 3.Find the value of f(1)

When $x = 1,$ the equation for is given by $f (x) = 2 x - 4$

Replace $x$ with $1$ in the function and simplify.

$f (1) = 2 (1) - 4 = 2 - 4 = - 2$

Therefore,the value of $f (1) = - 2$

Step 4.Find the value of f(2)

When $x = 2,$ the equation for is given by $f (x) = 2 x - 4$

Replace $x$ with $2$ in the function and simplify

$f (2) = 2 (2) - 4 = 4 - 4 = 0$

Therefor,the value of $f (2) = 0$

Step 5.Find the value of f(3)

When $x = 3,$ the equation for is given by $f (x) = x^{3} - 2$

Replace $x$ with $3$ in the function and simplify

role="math" localid="1645801017731" $f (3) = {(3)}^{3} - 2 = 27 - 2 = 25$

Therefore,the value of $f (3) = 25$

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If $f (x) = \{\begin{cases} 2 x - 4 i f - 1 \leq x \leq 2 \\ x^{3} - 2 i f 2 < x \leq 3 \end{cases}$
Find: (a) $f (0)$ (b) $f (1)$ (c) $f (2)$ (d) $f (3)$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Find the value of f(0)

Step 3.Find the value of f(1)

Step 4.Find the value of f(2)

Step 5.Find the value of f(3)

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If f(x)=2x-4if-1≤x≤2x3-2if2<x≤3Find: (a) f(0) (b) f(1) (c) f(2) (d)f(3)

Short Answer

Step by step solution

Step 1.Given information

Step 2.Find the value of f(0)

Step 3.Find the value of f(1)

Step 4.Find the value of f(2)

Step 5.Find the value of f(3)

One App. One Place for Learning.

Most popular questions from this chapter

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If $f (x) = \{\begin{cases} 2 x - 4 i f - 1 \leq x \leq 2 \\ x^{3} - 2 i f 2 < x \leq 3 \end{cases}$
Find: (a) $f (0)$ (b) $f (1)$ (c) $f (2)$ (d) $f (3)$