Chapter 2: Q. 26 (page 100)

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

Short Answer

Expert verified

(a) $6$

(b) $0$

Step by step solution

Step 1.Given information

The given function $f (x) = \{\begin{cases} - 3 x i f x < - 1 \\ 0 i f x = - 1 \\ 2 x^{2} + 1 i f x > - 1 \end{cases}$

Step 2. Finding the value of f(-2)

We observe that when $x = - 2$ the equation for $f$ is given by $f (x) = - 3 x$

Substitute $- 2$ for $x$ in the function and evaluate

$f (- 2) = - 3 (- 2) = 6$

Thus,the value of $f (- 2)$ is $6$ .

Step 3.Finding the value of f(-1)

We observe that when $x = - 1$ the equation for $f$ is given by $f (x) = 0$

$f (- 1) = 0$

Thus,the value of $f (- 1)$ is $0$

Step 4. Finding the value of f(0)

When $x = 0$ the the equation is.Evaluate

$f (0) = 2 x^{2} + 1 = 2 (0) + 1 = 1$

Thus,the value of $f (0)$ is $1$ .

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

Short Answer

Step by step solution

Step 1.Given information

Step 2. Finding the value of f(-2)

Step 3.Finding the value of f(-1)

Step 4. Finding the value of f(0)

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If f(x)=-3xifx<-10ifx=-12x2+1ifx>-1Find: (a)f(-2) and (b) f(-1) (c)f(0)

Short Answer

Step by step solution

Step 1.Given information

Step 2. Finding the value of f(-2)

Step 3.Finding the value of f(-1)

Step 4. Finding the value of f(0)

One App. One Place for Learning.

Most popular questions from this chapter

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