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disa [49]
3 years ago
6

Which of the following functions are one-to-one? Select all that apply.

Mathematics
2 answers:
Katyanochek1 [597]3 years ago
7 0
1,2 and 5 is the answers I think
olga2289 [7]3 years ago
5 0

Answer:

f(x)=x^3-7\,,\,f(x)=\frac{1}{8x-1} are one-to-one

Step-by-step explanation:

A function y = f(x) is said to be one-to-one if f(x_1)=f(x_2)\Rightarrow x_1=x_2

f(x)=x^3-7

f(x_1)=f(x_2)\\x_1^3-7=x_2^3-7\\x_1^3=x_2^3\\x_1=x_2

So, f is one-to-one.

f(x)=x^2-4

f(1)=1^2-4=1-4=-3\\f(-1)=(-1)^2-4=1-4=-3\\\Rightarrow f(1)=f(-1)\\\text{but}\,\,1\neq -1

So, f is not one-to-one

f(x)=\frac{1}{8x-1}

f(x_1)=f(x_2)\\\frac{1}{8x_1-1}=\frac{1}{8x_2-1}\\8x_1-1=8x_2-1\\8x_1=8x_2\\x_1=x_2

So, f is one-to-one

f(x)=\frac{5}{x^4}

f(1)=\frac{5}{1^4}=5\\f(-1)=\frac{5}{(-1)^4}=5\\f(1)=f(-1)\,\,but\\,\,1\neq -1

So, f is not one-to-one

f(x)=\left | x \right |

f(1)=\left | 1 \right |=1\\f(-1)=\left | -1 \right |=1\\f(1)=f(-1)\,\,but\,\,1\neq -1

So, f is not one-to-one

Therefore, functions f(x)=x^3-7\,,\,f(x)=\frac{1}{8x-1} are one-to-one

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Find the vertex and zeros of the following function f(x)=x^2-6x-7
elena-s [515]

Try this solution:

Step-by-step explanation:

1) for zeros of the function: x²-6x-7=0; ⇒ x₁=7; x₂= -1.

2) for the vertex of the function: x₀= -b/2a, where a;b;c - numbers from ax²+bx+c=0 (from x²-6x-7=0).

x₀=6/2=3;

y₀= (4ac-b²)/4a; ⇒ y₀= -16.

It means, the coordinates of the vertex are (3;-16).

6 0
3 years ago
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−13x+4y
stealth61 [152]
First start by writing th equation y=mx+b then because we know the slope (m) is perpendicular to the other line we can find it. so it would be the negative reciprocal to -13 which is 1/13 then you can use the slope and the x and y point and sub them into the equation to find the b value
y=3 x=4 m=1/13
3=1/13*4+b then solve for b
3=4/13+b
3-4/13=b
2.69=b
the write out the equation
y=1/13x+2.69
4 0
3 years ago
Read 2 more answers
PLS I NEED HELP I WILL REALLY APPRECIATE IF SOMEONE DID IT I WILL MARK YOU THE BRAINLY PLS HELP!!!!
VLD [36.1K]

Answer:

1) b= 39.5

2) c= 3.6

3) a=19

Step-by-step explanation:

Use the Pythagorean Theorem to find the missing side length.

"C" is the hypotenuse. Pythagorean Theorem: a^2+b^2=c^2

1) 11^2+b^2=c^41

121+b^2=1681

121-121+b^2=1681-121

b^2=1560

b= 39.5

2) 2^2+3^2=c^2

4+9=c^2

13=c^2

c= 3.6

3) a^2+9^2=21^2

a^2+81=441

a^2+81-81=441-81

a^2=360

a=19

Hope this helps!

5 0
2 years ago
Need help plz I'm stuck
Zolol [24]
What's your problem?
6 0
3 years ago
Read 2 more answers
Find the approximate solution(s) to each of the following equations graphically. Use technology to support your
11Alexandr11 [23.1K]

Answer: x = 3.05

Step-by-step explanation:

The picture shows the graphic solution using technology.

Verifying the approximate solution found on the graph.

x = 3.05

0.5x³ - 4 = 3x + 1

0.5(3.05)³ - 4 = 3(3.05) + 1

0.5*28.373 - 4 = 9.2 + 1

14.2 - 4 = 10.2

10.2 = 10.2 (ok)

3 0
3 years ago
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