Simplify the following expression.

The function f(x) is defined as follows: Determine the following values of the function. f(-3) = a0 and f(2) = a1 i

stellarik [79]

Question:

The function f(x) is defined as follows:

f(x)= 3x+1 if x is less than or equal to 0

2x^2 if 0 4 if c is greater than or equal to 2

determine the following values of the function

f(-3)= __

f(2)= ___

Answer:

The values are $f(-3)=-8$ and $f(2)=8$

Explanation:

The function is defined by two parts,

$f(x)=3 x+1$ if $x\leq 0$

$f(x)=2x^2$ if $x \geq 2$

To determine the value of $$f(-3)$ , we shall substitute the value $x=-3$ in the function $f(x)=3 x+1$ because $-3 \leq 0$

Hence, we have,

$f(x) \ \ =3 x+1\\f(-3)=3(-3)+1\\f(-3)=-9+1\\f(-3)=-8$

Now, to determine the value of $f(2)$ , we shall substitute the value $x=2$ in the function $f(x)=2x^2$ because $x \geq 2$

Hence, we have,

$f(x)=2 x^{2}\\f(2)=2\left(2^{2}\right)\\f(2)=2(4)\\f(2)=8$

Thus, the values are $f(-3)=-8$ and $f(2)=8$

3 0

3 years ago

kumpel [21]

One difference is that regrouping is often used for subtraction as partial pruducts is used when dividing

5 0

4 years ago

We choose a number from the set 1, 2, 3,..., 100 uniformly at random and denote this number by X. For each of the following choi

kiruha [24]

Answer:

(a) A and B are dependent.

(b) C and D are dependent.

(c) E and F are dependent.

Step-by-step explanation:

Two sets are said to be independent if the intersection of the two set is empty. That is the sets are disjoint.

Let's examine the situations to determine if they are independent or not.

(a) A = {2, 4, 6, . . . , 10, . . . , 20, . . .} and B = {5, 10, 15, . . . , 20, . . .}. Since A n B = {10, 20, . . .}, then the sets are dependent

(b) C = {10, 11, 12, . . . , 31, . . . , 62, . . . , 93, . . .} and D = {31, 62, 93}. Since C n D = {31, 62, 93}, then the sets are dependent.

(c) E = {5, 7, 11, . . .} and F = {5, 15, . . .}. Since E n F = {5}, then the set are dependent.

Thus

(a) A and B are dependent.

(b) C and D are dependent.

(c) E and F are dependent.

5 0

3 years ago

What is the area of the circle?

Gelneren [198K]

Answer:

For a circle.

Step-by-step explanation:

A=πr^2

7 0

3 years ago

Read 2 more answers

What is the equation of the line perpendicular to 3x+4y=12 and containing the point (6,-2)

tester [92]

3x+4y=12

4y = - 3x + 12

y = -3/4 x + 3; This line has slope equal - 3/4

Perpendicular lines, slope is opposite and reciprocal so slope of new line = 4/3

Passing point (6 , -2)

y + 2 = 4/3(x - 6)

y + 2 = 4/3 x - 8

y = 4/3 x - 10

Answer

Equation: y = 4/3 x - 10

6 0

3 years ago