All categories

3 years ago

If f(x) = -5x - 1 and g(x) = x - 6 what is (f g) (7)

Mathematics

2 answers:

Cloud [144]3 years ago

5 0

You have

$(f\circ g)(x) = f(g(x)) \implies (f\circ g)(7) = f(g(7))$

So, we have to compute g(7) and feed it as input to f(x). We have

$g(7)=7-6=1 \implies f(g(7))=f(1)=-5-1=-6$

Shtirlitz [24]3 years ago

4 0

Answer:

-6

Step-by-step explanation:

I just took it and got it right ☺

You might be interested in

PLEASE HELP ME I WILL GIVE BRAINLIEST JUST NO LINKS PLS!!

ruslelena [56]

Answer:b

Step-by-step explanation:

3 0

3 years ago

Hard question but would help me out

Alekssandra [29.7K]

Answer:

Critical value f(1)=2.

Minimum at (1,2), function is decreasing for $0$ and increasing for $x>1.$

$\left(3,\dfrac{4}{\sqrt{3}}\right)$ is point of inflection.

When 0<x<3, function is concave upwards and when x>3, , function is concave downwards.

Step-by-step explanation:

1. Find the domain of the function f(x):

$\left\{\begin{array}{l}x\ge 0\\x\neq 0\end{array}\right.\Rightarrow x>0.$

2. Find the derivative f'(x):

$f'(x)=\dfrac{(x+1)'\cdot \sqrt{x}-(x+1)\cdot (\sqrt{x})'}{(\sqrt{x})^2}=\dfrac{\sqrt{x}-\frac{x+1}{2\sqrt{x}}}{x}=\dfrac{2x-x-1}{2x\sqrt{x}}=\dfrac{x-1}{2x^{\frac{3}{2}}}.$

This derivative is equal to 0 at x=1 and is not defined at x=0. Since x=0 is not a point from the domain, the crititcal point is only x=1. The critical value is

$f(1)=\dfrac{1+1}{\sqrt{1}}=2.$

2. For $0$ the derivative f'(x)<0, then the function is decreasing. For $x>1,$ the derivative f'(x)>0, then the function is increasing. This means that point x=1 is point of minimum.

3. Find f''(x):

$f''(x)=\dfrac{(x-1)'\cdot 2x^{\frac{3}{2}}-(x-1)\cdot (2x^{\frac{3}{2}})'}{(2x^{\frac{3}{2}})^2}=$

$=\dfrac{2x^{\frac{3}{2}}-2(x-1)\cdot \frac{3}{2}x^{\frac{1}{2}}}{4x^3}=\dfrac{2x^{\frac{3}{2}}-2\cdot\frac{3}{2}x^{\frac{3}{2}}+ 2\cdot\frac{3}{2}x^{\frac{1}{2}}}{4x^3}=$

$=\dfrac{-x+3}{4x^{\frac{5}{2}}}.$

When f''(x)=0, x=3 and $f(3)=\dfrac{3+1}{\sqrt{3}}=\dfrac{4}{\sqrt{3}}.$

When 0<x<3, f''(x)>0 - function is concave upwards and when x>3, f''(x)>0 - function is concave downwards.

Point $\left(3,\dfrac{4}{\sqrt{3}}\right)$ is point of inflection.

4 0

4 years ago

PLEASE HELP!!!

Kaylis [27]

ANSWER

A reflection over the y-axis followed by a dilation by a factor greater than 1

EXPLANATION

We can see from the diagram that, square M and square P are all equal distance from the line y-axis.

This means that square M has been reflected in the y-axis.

Since square P is greater than square M, there has been a multiplication by a scale factor greater than 1.

The correct choice is B.

8 0

3 years ago

The length of a picture is 15.75 inches shorter than twice the width. If the perimeter of the picture is 106.5 inches, find its

Vladimir79 [104]

Answer:

Length = 45.37 in

Width = 30.56 in

Step-by-step explanation:

Let the width of the picture be 'w' inches.

Given:

Perimeter of the picture is, $P=106.5\ in$

Length is 15.75 inches shorter than twice the width. So, length is:

$l=2w-15.75$

Now, we know that the perimeter of a rectangular shape is given as the sum of all of its side. So, the picture is also of rectangular shape and hence the perimeter is given as:

$P=2l+2w$