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2 years ago

Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly?

2 answers:

6 0

If you want to find f[g(x)] just substitute "x+2" for an "x" in equation f(x)=7x+13. You'll get:

f[g(x)]= 7(x+2)+13=7x + 14 + 13 = 7x + 27

Choose second answer

LenKa [72]2 years ago

4 0

Answer:

B. f(g(x)) = 7x + 27

Step-by-step explanation:

We have, f(x) = 7x+13 and g(x) = x+2.

So, the function f(g(x)) is obtained by substituting the function g(x) = x+2 in f(x) = 7x+13,

i.e. f(g(x)) = f(x+2)

i.e. f(g(x)) = 7 × (x+2) + 13

i.e. f(g(x)) = 7x + 14 + 13

i.e. f(g(x)) = 7x + 27

Thus, f(g(x)) = 7x + 27

Hence, option B is correct.

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To make f continuous at x=2 , f(2) should be defined as what value? Justify your answer.

yawa3891 [41]

Answer:

To make f continuous at $x=2$ , $f(2)$ should be defined $x = 2.$

Step-by-step explanation:

A function, let say $f(x)$ , is defined at $x = c$ is continuous at $x = c$

If the limit of $f(x)$ as $x$ approaches $c$ is equal to the value of $f(x)$ at $x = c$ .

Mathematically it is written as:

$\lim _{x\to c}\:f\left(x\right)=f\left(c\right)$

then

$f(x)$ is continuous at $x = c$ .

So from the above definition, we conclude that:

To make f continuous at $x=2$ , $f(2)$ should be defined $x = 2.$

i.e.

$\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)$

then

$f(x)$ is continuous at $x = 2$ .

8 0

1 year ago

(iii) Find the smallest whole number h such that 4704/h is a cube number.

yan [13]

Answer:

$h=588$

Step-by-step explanation:

Given the fraction $\dfrac{4,704}{h}$

Consider its numerator and factor it:

$4,704=2^5\cdot 3\cdot 7^2$

You cann not take the cube root from $3, 7^2, 2^5,$ you can only take the cube root from $2^3$ , then the smallest whole number $h$ such that $\dfrac{4,704}{h}$ is a cube number is

$h=2^2\cdot 3\cdot 7^2=4\cdot 3\cdot 49=588$

When $h=588,$

$\dfrac{4,704}{588}=8=2^3$

6 0

1 year ago

At the start of the week, Monique’s savings account had a balance of $326. She made a $45 withdrawal each day for seven days. Du

sammy [17]

Answer:

Step-by-step explanation:

45 times 7= 315

326-315=11

125 times 2=250

250+11=261

so the answer is C. $261

6 0

2 years ago

Read 2 more answers

An expression is given: 2 open parentheses square root of k minus 1 close parenthesis plus square root of 8. If on adding negati

neonofarm [45]

Answer:

Possible value of k is √2

Step-by-step explanation:

The information given are;

The expression, 2·(√k - 1) + √8 to which may be added -6·√2 to obtain a rational number, we therefore have;

2·(√k - 1) + √8 - 6·√2 = R

Therefore, simplifying gives;

2·√k - 2 + 2·√2 - 6·√2 = 2·√k - 2 - 4·√2 = R

2·√k - 2 - 4·√2 + 2= R + 2 = R

2·√k - 2+ 2 - 4·√2 = R

2·√k + 0 - 4·√2 = 2·√k - 4·√2 = 2·(√k - 2·√2) = R

(√k - 2·√2) = R/2 = R

Therefore, √2 is a factor of √k such that √k - 2·√2 = R

Which gives k = x·√2, where x = a rational number

When x = 1, k = √2.

Therefore, a possible value of k is √2

3 0

2 years ago

A barber shop produces 96 haircuts a day. each barber in the shop works 8 hours per day and produces the same number of haircuts

Finger [1]

We know that
A barber shop produces 96 haircuts a day----------> 8 hours per day
so
96/8--------> 12 haircuts per hour

if if the shop's productivity is 2 haircuts per hour of labor
then
12/2---------> 6 barbers

the answer is
6 barbers

7 0

2 years ago